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Metric invariants and space structures

Research Project

Project/Area Number 17540079
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionOkayama University of Science

Principal Investigator

SAKAI Takashi  Okayama University of Science, FACULTY OF SCIENCE, PROFESSOR (70005809)

Co-Investigator(Kenkyū-buntansha) KIYOHARA Kazuyoshi  OKAYAMA UNIVERSITY, FACULTY OF SCIENCE, PROFESSOR (80153245)
ITOH Jin-ichi  KUMAMOTO UNIVERSITY, FACULTY OF EDUCATION, PROFESSOR (20193493)
KATSUDA Atsushi  OKAYAMA UNIVERSITY, FACULTY OF SCIENCE, ASSOCIATE PROFESSOR (60183779)
MORI Yoshiyuki  OKAYAMA UNIVERSITY OF SCIENCE, FACULTY OF SCIENCE, LECTURER (00388919)
Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥3,700,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2005: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsRiemannian manifolds / Distance functions / Morse theory / Geodesics / Cut loci
Research Abstract

Distance function d_p to a point p of a compact Riemannian manifold is an important geometric function that is also related to the manifold structure. However, distance function d_p admits a point where d_p is not differentiable, and such a point is contained in the cut locus C_p of p. It was known that the notion of critical points may be introduced as in usual Morse theory and d_p is not differentiable at critical points. In the case where there are no critical points, Morse theory (the isotopy lemma) has been developed as in smooth case that played an important role in applications.
Now to develop Morse theory for distance functions including critical points, one should first define the notion of the index at a critical point. Under the support of the present Grant-in-Aid, T. Sakai, head investigator of this research program, carried out this with J. Itoh when Riemannian metric satisfies some natural non-degeneracy conditions, and developed Morse theory for distance functions from a … More direct geometric view point (has been published in a Journal). There it is important to show that the cut locus Cp carries a nice structure (Whitney stratification), and the index of a critical point q is defined in terms of the number of minimal geodesics joining p, q and the usual index at q of the restriction of 4 to the stratum containing q that is a smooth function with a critical point q. I hope to continue to study how generic is the conditions among all Riemannian metrics on a given manifold.
With respect to distance functions, K. Kiyohara determined the explicit structure of the cut locus and the conjugate locus of any point in ellipsoids (and some Liouville manifolds) from a view point of integrable geodesic flow with J. Itoh, and A. Katsuda studied the inverse problem of the Neumann boundary value problem, namely how to reconstruct the inner Riemannian metric from the distance function to the boundary of a Riemannian manifold with boundary.
As for geometric inequalities (isosystolic inequality, isodiametric inequality) and the first eigenvalue estimate of the Laplacian of a compact Riemannian manifolds with non-negative Ricci curvature and its perturbation, we could not make substantial progress in this period, but Kiyohara obtained a result concerning an inequality of geometric invariants of Alexandrov spaces. I hope to continue to carry the program. Y. Mori investigated algorithm of quantum computer and supported Sakai in computer aid. Less

Report

(4 results)
  • 2007 Annual Research Report   Final Research Report Summary
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (153 results)

All 2010 2008 2007 2006 2005 Other

All Journal Article (62 results) (of which Peer Reviewed: 28 results) Presentation (85 results) Book (6 results)

  • [Journal Article] Criteria for farthest points on convex surfaces2010

    • Author(s)
      J. Itoh, C. Vilcu
    • Journal Title

      Math.Nachrichten (発行予定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Antipodal convex hypersurfaces2010

    • Author(s)
      J. Itoh, J. Rouyer, C. Vilcu
    • Journal Title

      Indagationes Math (発行予定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The total absolute curvature of open curves in E^32008

    • Author(s)
      K.Enomoto, J.Itoh, R.Sinclair
    • Journal Title

      Illinois J.of Math. (発行確定)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] The total absdlute curvature of open culves in E^32008

    • Author(s)
      K. Enomoto, J. Itoh, R. Sindai
    • Journal Title

      Illinois J.of Math. (発行予定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 書評:M.Berger;A Panoramic View of Riemannian Geometry,Springer,2003年,XXIII+824ページ2007

    • Author(s)
      酒井 隆
    • Journal Title

      数学 59

      Pages: 216-221

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Cut loci and distance functions2007

    • Author(s)
      J.Itoh, T.Sakai
    • Journal Title

      Math.J.Okayama Univ. 19

      Pages: 65-92

    • NAID

      120002309399

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Manifolds with simple cut loci2007

    • Author(s)
      J.Itoh, K.Kiyohara
    • Journal Title

      Rev.Bull.Cal.Math.Soc. 15

      Pages: 61-64

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Acute triangulations of the regular dodecahedral surface2007

    • Author(s)
      J.Itoh, T.Zamfirescu
    • Journal Title

      Europian J.of Combinatorics 28

      Pages: 1072-1086

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging 1

      Pages: 135-157

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Effective error correction method for quantum information processing2007

    • Author(s)
      M.Kawamura, Y.Mori and others
    • Journal Title

      International Journal of Quantum Chemistry 107

      Pages: 3067-3070

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Book Review : M. Berger ; A Panoramic View of Riemannian Geometry Springer, 2003, XXIII + 824(in Japanese)2007

    • Author(s)
      T. Sakai
    • Journal Title

      Sugaku 59-2

      Pages: 216-221

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Cut loci and distance functions2007

    • Author(s)
      J. Itoh, T. Sakai.
    • Journal Title

      Math. J. Okayama Univ. 49

      Pages: 65-92

    • NAID

      120002309399

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Manifolds with simple cut loci2007

    • Author(s)
      J. Itoh, K. Kiyohara
    • Journal Title

      Rev. Bull. Cal Math. Soc. 15-1

      Pages: 61-64

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Acute triangulations of the regular dodecahedral surface2007

    • Author(s)
      J. Itoh, T. Zamfirescu
    • Journal Title

      Europian J. of Combinatorics 28

      Pages: 1072-1086

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. Kurylev, M. Lassas
    • Journal Title

      Inverse Problems and Imaging 1-1

      Pages: 135-157

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Effective error correction method for quantum information processing2007

    • Author(s)
      M. Kawamura, T. Morimoto, Y. Mori, R. Sawae, K. Takarabe, Y. Manmoto, T. Sakata
    • Journal Title

      International J. of Quantum Chemistry 107

      Pages: 3067-3070

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] One can see the topology looking at the curvature2007

    • Author(s)
      T. Sakai(coauthor)
    • Journal Title

      Solution of the Poincare Conjecture(Special Issue of SugakwSeminar). Nippon-Hyoron-Sha

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Bergen Esprit of Geometry2007

    • Author(s)
      T. Sakai(coauthor)
    • Journal Title

      Currents of Modern Geometry (ed., T. Sunada). Nippon- Hyoron-Sha

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] 書言平:M.Berger;A Panoramic View of Riemannian Geometry,Springer,2003年,XXIII+824ページ2007

    • Author(s)
      酒井 隆
    • Journal Title

      数学 59

      Pages: 216-221

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cut loci and distance functions2007

    • Author(s)
      J. Itoh, T. Sakai
    • Journal Title

      Math.J.Okayama Univ 49

      Pages: 65-92

    • NAID

      120002309399

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Manifolds with simple cut loci2007

    • Author(s)
      J. Itoh, K. Kiyohara
    • Journal Title

      Rev.Bull.Cal.Math.Soc. 15

      Pages: 61-64

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Acute triangulations of the regular dodecahedral surface2007

    • Author(s)
      J. Itoh, T. Zamfirescu
    • Journal Title

      Europian J.of Combinatorics 28

      Pages: 1072-1086

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. Kurylev, M. Lassas
    • Journal Title

      Inverse Problems and Imaging 1

      Pages: 135-157

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Effective error correction method for quantum information processing2007

    • Author(s)
      M. Kawamura, Y. Mori, others
    • Journal Title

      International Journal of Quantum Chemistry 107

      Pages: 3067-3070

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cut loci and distance functions2007

    • Author(s)
      J.Itoh, T.Sakai
    • Journal Title

      Mathematical Journal of Okayama Univ. 49(To appear)

    • NAID

      120002309399

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Probl.Imaging 1・1

      Pages: 135-157

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 書評:M. Berger : A panoramic View of Riemannian Geometry, Springer, 2003年, XXIII+824ページ2007

    • Author(s)
      酒井 隆
    • Journal Title

      数学 59巻2号

      Pages: 216-221

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 直線と幾何学-真っ直ぐなものと曲がったもの-2006

    • Author(s)
      酒井 隆
    • Journal Title

      数学通信 10

      Pages: 5-23

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Periodic geodesic flows and integrable geodesic flows2006

    • Author(s)
      K.Kiyohara
    • Journal Title

      Sugaku Expositions 19

      Pages: 105-116

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Tightness of graphs2006

    • Author(s)
      J.Itoh, W.Kuhnel
    • Journal Title

      Review Roumaine Math.Pures et Appliques 51

      Pages: 1-19

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Tetrahedra passing through a circular or square hole2006

    • Author(s)
      J.Itoh, Y.Tanoue, T.Zamfirescu
    • Journal Title

      Rendiconti del Circolo Matematico di Palermo, Suppl. 77

      Pages: 349-354

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On the length of simple closed quasigeodesics on convex surfaces2006

    • Author(s)
      J.Itoh, C.Vilcu
    • Journal Title

      Comptes Rendus Math. 343

      Pages: 259-264

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Decoherence of a Greenberger-Horne-Zeilinger state in a fivequbit NMR Quantum Computer2006

    • Author(s)
      M.Kawamura, Y.Mori and others
    • Journal Title

      International Journal of Quantum Chemistry 106

      Pages: 3108-3112

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Lines and geometry-what is straight and what is curved(in Japanese)2006

    • Author(s)
      T. Sakai
    • Journal Title

      Sugaku Tsusin 10-4

      Pages: 5-23

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Periodic geodesic flows and integrable geodesic flows2006

    • Author(s)
      K. Kiyohara
    • Journal Title

      Sugaku Expositions 19-1

      Pages: 105-116

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Tightness of graphs2006

    • Author(s)
      J. Itoh, W. Kuhnel
    • Journal Title

      Review Roumaine Math. Pures et Appliques 51

      Pages: 1-19

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Tetrahedra passing through a circular or square hole2006

    • Author(s)
      J. Itoh, Y. Tanoue, T. Zamfirescu
    • Journal Title

      Rendiconti del Circolo Matematico di Palermo, Suppi. 77

      Pages: 349-354

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On the length of simple closed quasigeodesics on convex surfaces2006

    • Author(s)
      J. Itoh, C. Vilcu
    • Journal Title

      Comptes Rendus Math. 343

      Pages: 259-264

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Decoherence of a Greenberger-Horne-Zeilinger state in a fivequbit NMR Quantum Computer2006

    • Author(s)
      M. Kawamura, T. Morimoto, Y. Mori, R. Sawae, K. Takarabe, Y. Manmoto
    • Journal Title

      International J. of Quantum Chemistry 106

      Pages: 3108-3112

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Tighteness of graphs : realisations with the two-piece-property.2006

    • Author(s)
      J.Itoh, W.Kuhnel
    • Journal Title

      Rev.Roumaine Math.Pures Appl 51・1

      Pages: 1-19

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On the length of simple closed quasigeodesics on convwx surfaces2006

    • Author(s)
      J.Itoh, C.Vilcu
    • Journal Title

      C.R.Math.Acid.Sci.Paris 343・4

      Pages: 349-354

    • Related Report
      2006 Annual Research Report
  • [Journal Article] "直線"と幾何学-真っ直ぐなものと曲がったもの-2006

    • Author(s)
      酒井 隆
    • Journal Title

      数学通信(日本数学会) 10・4

      Pages: 5-23

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Curvature-up through the twentieth century,and its future2005

    • Author(s)
      T.Sakai
    • Journal Title

      Sugaku Expositions 18

      Pages: 165-187

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Appendix to:"Some metric invariants of spheres and Alexandrov spacesII"[Math.J.Okayama Univ.,47(2005),193-202]by N.Sochi2005

    • Author(s)
      K.Kiyohara
    • Journal Title

      Math.J.Okayama Univ. 47

      Pages: 189-191

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] On the length of the cut locus for finitely many points2005

    • Author(s)
      J.Itoh, T.Zamfirescu
    • Journal Title

      Advances in Geometry 5

      Pages: 97-106

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Gauss-type curvatures and tubes for polyhedral surfaces2005

    • Author(s)
      J.Itoh
    • Journal Title

      Kumamoto J.Math. 18

      Pages: 51-56

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary 2005 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Total curvature of noncompact piecewise Riemannian 2-polyhedra2005

    • Author(s)
      J.Itoh, F.Ohtsuka
    • Journal Title

      Tsukuba J.Math. 29

      Pages: 471-493

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary 2005 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Simplicies passing through a hole2005

    • Author(s)
      J.Itoh, T.Zamfirescu
    • Journal Title

      J.of Geometry 83

      Pages: 65-70

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Quantum Circuits for an Effective Pure State in NMR Quantum Computer2005

    • Author(s)
      Y.Mori, R.Sawae and others
    • Journal Title

      International Journal of Quantum Chemistry 105

      Pages: 758-761

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
    • Peer Reviewed
  • [Journal Article] Curvature-up through the twentieth century, and the future?2005

    • Author(s)
      T. Sakai
    • Journal Title

      Sugaku Expositions 18-2

      Pages: 165-187

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Appendix to : Some metric invariants of spheres and Alexandrov spaces II[Math. J. Okayama Univ., 47(2005), 193-202] by N. Sochi2005

    • Author(s)
      K. Kiyohara
    • Journal Title

      Math. J. Okayama Univ. 47

      Pages: 189-191

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] On the length of the cut locus for finitely many points2005

    • Author(s)
      J. Itoh, T. Zamfirescu
    • Journal Title

      Advances in Geometry 5

      Pages: 97-106

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Gauss-type curvatures and tubes for polyhedral surfaces2005

    • Author(s)
      J. Itoh
    • Journal Title

      Kumamoto J. Math. 18

      Pages: 51-56

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Total curvature of noncompact piecewise Riemannian 2-polyhedra2005

    • Author(s)
      J. Itoh, F. Ohtsuka
    • Journal Title

      Tsukuba J. Math. 29

      Pages: 471-493

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Simplicies passing through a hole2005

    • Author(s)
      J. Itoh, T. Zamfirescu
    • Journal Title

      J. of Geometry 83

      Pages: 65-70

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Quantum Circuits for an Effective Pure State in NMR Quantum Computer2005

    • Author(s)
      Y. Mori, R. Sawae, M. Kawamura, T. Sakata, K. Takarabe
    • Journal Title

      International J. of Quantum Chemistry 105

      Pages: 758-761

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Appendix to "Some metric invariants of spheres and Alexandrov spaces II"2005

    • Author(s)
      K.Kiyohara
    • Journal Title

      Math.J.Okayama Univ. 4

      Pages: 189-191

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Simplices passing through a hole2005

    • Author(s)
      J.Itoh, T.Zamfirescu
    • Journal Title

      J.Geometry 83

      Pages: 65-70

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Quantum circuits for an effective pure state in NMR quantum computer2005

    • Author(s)
      Y.Mori, R.Sawae, M.Kawamura, T.Sakata, K.Takarabe
    • Journal Title

      J.Quantum Chemistry 105

      Pages: 758-761

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The total absolute curvature of open curves in E^3

    • Author(s)
      K. Enomoto, J. Itoh, R. Sinclair
    • Journal Title

      Illinois J. of Math. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Criteria for farthest points on convex surfaces

    • Author(s)
      J. Itoh, C. Vilcu
    • Journal Title

      Math. Nachrichten (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Journal Article] Antipodal convex hypersurfaces

    • Author(s)
      J. Itoh, J. Rouyer, C. Vilcu
    • Journal Title

      Indagationes Math. (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Zeros of Jacobi fields on ellipsoids and some Liouville manifolds2008

    • Author(s)
      K. Kiyohara
    • Organizer
      Problems on geodesics and related topics
    • Place of Presentation
      Kumamoto Univ
    • Year and Date
      2008-06-06
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 楕円体上の共役跡と共役点の漸近分布2008

    • Author(s)
      清原 一吉
    • Organizer
      大阪市立大学微分幾何学セミナー
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2008-01-16
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Conjugate loci and asymptotic distribution of conjugate points on ellipsoids2008

    • Author(s)
      K. Kiyohara
    • Organizer
      Differential Geometry Seminar of Osaka City Univ.
    • Place of Presentation
      Osaka City Univ
    • Year and Date
      2008-01-16
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Zeros of Jacobi fields on ellipsoids and some Liouville manifolds2008

    • Author(s)
      清原 一吉
    • Organizer
      「測地線および関連する諸問題」研究集会
    • Place of Presentation
      熊本大学教育学部
    • Year and Date
      2008-01-06
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] The conjugate loci on ellipsoids and some Liouville manifolds2007

    • Author(s)
      清原 一吉
    • Organizer
      International symposium on recent advances in mathematics and its applications(ISRAMA 2007)
    • Place of Presentation
      Calcutta Mathematical Society
    • Year and Date
      2007-12-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Simple geodesics on convex surfaces2007

    • Author(s)
      伊藤 仁一
    • Organizer
      International symposium on recent advances in mathematics and its applications
    • Place of Presentation
      Calcutta,India
    • Year and Date
      2007-12-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The conjugate loci on ellipsoids and some Liouville manifolds2007

    • Author(s)
      K. Kiyohara
    • Organizer
      international symposium on recent advances in mathematics and its applications
    • Place of Presentation
      Calcutta Math. Soc
    • Year and Date
      2007-12-15
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Simple geodesics on convex surfaces2007

    • Author(s)
      J. Itoh
    • Organizer
      International symposium on recent advances in mathematics and its applications
    • Place of Presentation
      Calcutta, India
    • Year and Date
      2007-12-15
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The conjugate loci on ellipsoids and some Liouville manifolds2007

    • Author(s)
      清原 一吉
    • Organizer
      International symposium on recent advances in Mathematics and its applications(ISRAMA2007)
    • Place of Presentation
      Calcutta Mathematical Society
    • Year and Date
      2007-12-15
    • Related Report
      2007 Annual Research Report
  • [Presentation] Simple geodesics on convex surfaces2007

    • Author(s)
      伊藤 仁一
    • Organizer
      International Symposium on Recent Advances in Mathematics and its Applications
    • Place of Presentation
      Calcutta,India
    • Year and Date
      2007-12-15
    • Related Report
      2007 Annual Research Report
  • [Presentation] Acute triangulations on flat tori2007

    • Author(s)
      伊藤 仁一
    • Organizer
      第19回位相幾何学的グラフ理論研究集会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2007-11-16
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Acute triangulations on flat tori2007

    • Author(s)
      J. Itoh
    • Organizer
      19th Topological graph theory seminar
    • Place of Presentation
      Yokohama National Univ
    • Year and Date
      2007-11-16
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Acute trianguiations on flat tori2007

    • Author(s)
      伊藤 仁一
    • Organizer
      第19回位相幾何学的グラフ理論研究集会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2007-11-16
    • Related Report
      2007 Annual Research Report
  • [Presentation] Tetrahedra passing through a circular or square hole2007

    • Author(s)
      伊藤 仁一, 田上 雄一, T.Zamfirescu
    • Organizer
      日本数学会秋季総合分科会幾何学分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Simplices passing through a hole2007

    • Author(s)
      伊藤 仁一, T.Zamfirescu
    • Organizer
      日本数学会秋季総合分科会幾何学分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-23
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Tetrahedra passing through a circular or square hole2007

    • Author(s)
      J. Itoh, Y. Tanoue, T. Zamfirescu
    • Organizer
      Autumn meeting of Math. Soc. Japan
    • Place of Presentation
      Tohoku Univ
    • Year and Date
      2007-09-23
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Simplices passing through a hole2007

    • Author(s)
      J. Itoh, T. Zamfirescu
    • Organizer
      Autumn meeting of Math. Soc. Japan
    • Place of Presentation
      Tohoku Univ
    • Year and Date
      2007-09-23
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Several topics of space curves and cut loci on ellipsoids2007

    • Author(s)
      伊藤 仁一
    • Organizer
      Geometry Seminar at IMAR
    • Place of Presentation
      Bucharest,Romania
    • Year and Date
      2007-09-12
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Several topics of space curves and cut loci on ellipsoids2007

    • Author(s)
      J. Itoh
    • Organizer
      Geometry Seminar at IMAR
    • Place of Presentation
      Bucharest, Romania
    • Year and Date
      2007-09-12
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The cut loci and the conjugate loci on ellipsoids and some Liouville manifolds2007

    • Author(s)
      清原 一吉
    • Organizer
      10th International conference"Differential Geometry and Its Applications"
    • Place of Presentation
      パラキ大学(チェコ・オロモウツ)
    • Year and Date
      2007-08-31
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The cut loci and the conjugate loci on ellipsoids and some Liouville manifolds2007

    • Author(s)
      K. Kiyohara
    • Organizer
      10th International conference Differential Geometry and Its Applications
    • Place of Presentation
      Palacky Univ., Olomouc, Czech
    • Year and Date
      2007-08-31
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The cut loci and the conjugate loci on ellipsoids and some Liouville manifolds2007

    • Author(s)
      清原 一吉
    • Organizer
      10th International conference"Differential Geoometry and Its Applications"
    • Place of Presentation
      パラキ大学(チェコ・オロモウツ)
    • Year and Date
      2007-08-31
    • Related Report
      2007 Annual Research Report
  • [Presentation] An overview of Sunada's works2007

    • Author(s)
      勝田 篤
    • Organizer
      Spectral Analysis in Geometry and Number theory
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-08-07
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] An overview of Sunada's works2007

    • Author(s)
      A. Katsuda
    • Organizer
      Spectral Analysis in Geometry and Number Theory
    • Place of Presentation
      Nagoya Univ
    • Year and Date
      2007-08-07
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Spectral Analysis in Geometry2007

    • Author(s)
      勝田 篤
    • Organizer
      第17回岡山幾何学談話会
    • Place of Presentation
      岡山大学
    • Year and Date
      2007-07-27
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Spectral Analysis in Geometry2007

    • Author(s)
      A. Katsuda
    • Organizer
      Okayama Colloquium on Geometry
    • Place of Presentation
      Okayama Univ
    • Year and Date
      2007-07-27
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Geodesic characterization of the isosceles tetrahedron2007

    • Author(s)
      伊藤 仁一
    • Organizer
      10th International conference on discrete mathematics
    • Place of Presentation
      Dortmund,Germany
    • Year and Date
      2007-07-08
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Presentation] Geodesic characterization of the isosceles tetrahedron2007

    • Author(s)
      J. Itoh
    • Organizer
      10th International conf. on discrete math.
    • Place of Presentation
      Dortmund, Germany
    • Year and Date
      2007-07-08
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Behavior of geodesics and the conjugate loci on ellipsoids2007

    • Author(s)
      清原 一吉
    • Organizer
      Seminar on Functional analysis and Global analysis
    • Place of Presentation
      東京理科大学理工学部
    • Year and Date
      2007-06-06
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Behavior of geodesics and the conjugate loci on ellipsoids2007

    • Author(s)
      K. Kiyohara
    • Organizer
      Seminar on Functional analysis and Global analysis
    • Place of Presentation
      Tokyo Univ. of Sci
    • Year and Date
      2007-06-06
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Behavior of geodesics and the conjugate loci on ellipsoids2007

    • Author(s)
      清原 一吉
    • Organizer
      Seminar on Functional analysis and Globalanalysis
    • Place of Presentation
      東京理科大学理工学部
    • Year and Date
      2007-06-06
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the length of simple closed quasigeodesics on convex surfaces2007

    • Author(s)
      伊藤 仁一, C.Vilcu
    • Organizer
      日本数学会年会幾何学分科会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2007-03-29
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the length of simple closed quasigeodesics on convex surfaces2007

    • Author(s)
      J. Itoh, C. Vilcu
    • Organizer
      Annual meeting of Math. Soc. Japan
    • Place of Presentation
      Saitama Univ
    • Year and Date
      2007-03-29
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Every point is critical2007

    • Author(s)
      伊藤 仁一
    • Organizer
      「幾何構造と部分多様体の交差する領域」研究会
    • Place of Presentation
      名城大学
    • Year and Date
      2007-03-08
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Every point is critical2007

    • Author(s)
      J. Itoh
    • Organizer
      Geometric structures and submanifolds
    • Place of Presentation
      Meijyo Univ
    • Year and Date
      2007-03-08
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 種数2の閉曲面に対する等縮不等式2007

    • Author(s)
      酒井 隆
    • Organizer
      福岡微分幾何学研究集会
    • Place of Presentation
      福岡大学セミナーハウス
    • Year and Date
      2007-02-01
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Isosystolic inequality for surface of genus 22007

    • Author(s)
      T. Sakai
    • Organizer
      Fukuoka Seminar on Differential Geometry
    • Place of Presentation
      Fukuoka Univ. Seminar House
    • Year and Date
      2007-02-01
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Cut locus and several topics of intuitive geometry2007

    • Author(s)
      伊藤 仁一
    • Organizer
      Geometry Seminar at Dortmund Univ.
    • Place of Presentation
      Dortmund,Germany
    • Year and Date
      2007-01-15
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Cut locus and several topics of intuitive geometry2007

    • Author(s)
      J. Itoh
    • Organizer
      Geometry Seminar at Dortmund Univ.
    • Place of Presentation
      Dortmund, Germany
    • Year and Date
      2007-01-15
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] リウヴィル多様体の測地線の挙動2007

    • Author(s)
      清原 一吉
    • Organizer
      筑波大学数学系幾何学セミナー
    • Place of Presentation
      筑波大学
    • Year and Date
      2007-01-08
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Behavior of geodesics on Liouville manifolds2007

    • Author(s)
      K. Kiyohara
    • Organizer
      Geometry Seminar of Tsukuba Univ. Math. Dept.
    • Place of Presentation
      Tsukuba Univ
    • Year and Date
      2007-01-08
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Cut locus and geodesics on convex surfaces2006

    • Author(s)
      伊藤 仁一
    • Organizer
      Geometry Seminar at Kiel Univ.
    • Place of Presentation
      Kiel,Germany
    • Year and Date
      2006-12-20
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Cut locus and geodesics on convex surfaces2006

    • Author(s)
      J. Itoh
    • Organizer
      Geometry Seminar at Kiel Univ.
    • Place of Presentation
      Kiel, Germany
    • Year and Date
      2006-12-20
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Manifolds with simple cut loci2006

    • Author(s)
      清原 一吉
    • Organizer
      International symposium on recent advances in mathematics and its applications(ISRAMA 2006)
    • Place of Presentation
      Calcutta Mathematical Society
    • Year and Date
      2006-12-17
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Manifolds with simple cut loci2006

    • Author(s)
      K. Kiyohara
    • Organizer
      International symposium on recent advances in mathematics and its applications
    • Place of Presentation
      Calcutta Math. Soc
    • Year and Date
      2006-12-17
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] リウヴィル多様体のカットローカスとヤコビ場2006

    • Author(s)
      清原 一吉
    • Organizer
      「測地線および関連する諸問題」研究集会
    • Place of Presentation
      熊本大学教育学部
    • Year and Date
      2006-10-29
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Cut loci and Jacobi fields of Liouville manifolds2006

    • Author(s)
      K. Kiyohara
    • Organizer
      Problems on geodesics and related topics
    • Place of Presentation
      Kumamoto Univ
    • Year and Date
      2006-10-29
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 単純なカットローカスを持つ多様体2006

    • Author(s)
      清原 一吉
    • Organizer
      幾何学研究集会
    • Place of Presentation
      広島大学
    • Year and Date
      2006-10-06
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Manifolds with simple cut loci2006

    • Author(s)
      K. Kiyohara
    • Organizer
      Hiroshima Geometry Seminar
    • Place of Presentation
      Hiroshima Univ
    • Year and Date
      2006-10-06
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Every point is critical2006

    • Author(s)
      伊藤 仁一, I.Barany, C.Vilcu, T.Zamfirescu
    • Organizer
      日本数学会秋季総合分科会幾何学分科会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2006-09-20
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Every point is critical2006

    • Author(s)
      J. Itoh, I. Barany, C. Vilcu, T. Zamfirescu
    • Organizer
      Autumn meeting of Math. Soc. Japan
    • Place of Presentation
      Osaka City Univ
    • Year and Date
      2006-09-20
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Every point is critical2006

    • Author(s)
      伊藤 仁一
    • Organizer
      Workshop on Geometric and Topological Combinatorics
    • Place of Presentation
      Alcala de Henares,Spain
    • Year and Date
      2006-09-01
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Every point is critical2006

    • Author(s)
      J. Itoh
    • Organizer
      Workshop on Geom. and Topol. Combinat.
    • Place of Presentation
      Alcala de Henares, Spain
    • Year and Date
      2006-09-01
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 単純なカットローカスを持つ多様体2006

    • Author(s)
      清原 一吉
    • Organizer
      第53回幾何学シンポジウム
    • Place of Presentation
      金沢大学
    • Year and Date
      2006-08-06
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Manifolds with simple cut loci2006

    • Author(s)
      K. Kiyohara
    • Organizer
      The 53th Geometry Symposium
    • Place of Presentation
      Kanazawa Univ
    • Year and Date
      2006-08-06
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 閉じていない空間曲線の絶対全曲率2006

    • Author(s)
      榎本 一之, 伊藤 仁一, R.Sinclair
    • Organizer
      日本数学会年会幾何学分科会
    • Place of Presentation
      中央大学
    • Year and Date
      2006-03-26
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] The total absolute curvature of open space curves2006

    • Author(s)
      K. Enomoto, J. Itoh, R. Sinclair
    • Organizer
      Annual meeting of Math. Soc. Japan
    • Place of Presentation
      Chuo Univ
    • Year and Date
      2006-03-26
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Several topics of space curves and geodesics2006

    • Author(s)
      伊藤 仁一
    • Organizer
      Geometry Seminar at T.U.Denmark
    • Place of Presentation
      Copenhagen,Denmark
    • Year and Date
      2006-03-16
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Several topics of space curves and geodesics2006

    • Author(s)
      J. Itoh
    • Organizer
      Geometry Seminar at T. U. Denmark
    • Place of Presentation
      Copenhagen, Denmark
    • Year and Date
      2006-03-16
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Geodesic characterizations of isosceles tetrahedra2006

    • Author(s)
      伊藤 仁一, C.Vilcu
    • Organizer
      「等質空間の幾何学的諸相」研究会
    • Place of Presentation
      名城大学
    • Year and Date
      2006-03-04
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Geodesic characterizations of isosceles tetrahedra2006

    • Author(s)
      J. Itoh, C. Vilcu
    • Organizer
      Aspects of geometry of homogeneous spaces
    • Place of Presentation
      Meijyo Univ
    • Year and Date
      2006-03-04
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] リウヴィル多様体のカットローカス2006

    • Author(s)
      清原 一吉
    • Organizer
      「等質空間の幾何学の諸相」研究集会
    • Place of Presentation
      名城大学
    • Year and Date
      2006-03-03
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Cut loci of Liouville manifolds2006

    • Author(s)
      K. Kivohara.
    • Organizer
      Aspects of geometry of homogeneous spaces
    • Place of Presentation
      Meijyo Univ
    • Year and Date
      2006-03-03
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] リウヴィル多様体のカットローカス2006

    • Author(s)
      清原 一吉
    • Organizer
      「測地線および関連する諸問題」研究集会
    • Place of Presentation
      熊本大学教育学部
    • Year and Date
      2006-01-08
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Cut loci of Liouville manifolds2006

    • Author(s)
      K. Kiyohara
    • Organizer
      Problems on geodesics and related topics
    • Place of Presentation
      Kumamoto Univ
    • Year and Date
      2006-01-08
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Locating farthest points on convex surfaces2005

    • Author(s)
      伊藤 仁一
    • Organizer
      International Workshop on Differential Geometry
    • Place of Presentation
      佐賀大学
    • Year and Date
      2005-12-24
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Locating farthest points on convex surfaces2005

    • Author(s)
      J. Itoh
    • Organizer
      International Workshop on Diff. Geom.
    • Place of Presentation
      Saga University
    • Year and Date
      2005-12-24
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 距離関数のMorse理論とcut locus2005

    • Author(s)
      酒井 隆
    • Organizer
      研究集会「多様体上の微分方程式」
    • Place of Presentation
      金沢大学サテライト・プラザ講義室
    • Year and Date
      2005-12-12
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Morse theory of distance functions and cut loci2005

    • Author(s)
      T. Sakai
    • Organizer
      Differential Equations on Manifolds
    • Place of Presentation
      Satelite Plaza of Kanazawa Univ
    • Year and Date
      2005-12-12
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Locating farthest points on convex surfaces2005

    • Author(s)
      家入 幸喜, 伊藤 仁一, C.Vilcu
    • Organizer
      日本数学会秋季総合分科会幾何学分科会
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-21
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Locating farthest points on convex surfaces2005

    • Author(s)
      K. Ieiri, J. Itoh, C Vilcu
    • Organizer
      Autumn meeting of Math. Soc. Japan
    • Place of Presentation
      Okayama Univ
    • Year and Date
      2005-09-21
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 直線と幾何学-真っ直ぐなものと曲がったもの-2005

    • Author(s)
      酒井 隆
    • Organizer
      2005年秋の日本数学会市民講演会
    • Place of Presentation
      岡山大学
    • Year and Date
      2005-09-18
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Lines and geometry-what is straight and what is curved2005

    • Author(s)
      T. Sakai
    • Organizer
      Math. Soc. of Japan Lecture for Citizens
    • Place of Presentation
      Okayama Univ
    • Year and Date
      2005-09-18
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Cut loci and farthest points on surfaces2005

    • Author(s)
      伊藤 仁一
    • Organizer
      Geometry Seminar at T.U.Denmark
    • Place of Presentation
      Copenhagen,Denmark
    • Year and Date
      2005-09-09
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Cut loci and farthest points on surfaces2005

    • Author(s)
      J. Itoh
    • Organizer
      Geometry Seminar at T. U. Denmark
    • Place of Presentation
      Copenhagen, Denmark
    • Year and Date
      2005-09-09
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Farthest points and cut loci on surfaces2005

    • Author(s)
      伊藤 仁一
    • Organizer
      The 5th Conference of Balkan Society of Geometry
    • Place of Presentation
      Mangaria,Romania
    • Year and Date
      2005-08-30
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Farthest points and cut loci on surfaces2005

    • Author(s)
      J. Itoh
    • Organizer
      The 5th Conference of Balkan Society of Geo-metry.
    • Place of Presentation
      Mangaria, Romania
    • Year and Date
      2005-08-30
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Gel'fandのスペクトル逆問題の安定性について2005

    • Author(s)
      勝田 篤
    • Organizer
      東北大学幾何セミナー
    • Place of Presentation
      東北大学
    • Year and Date
      2005-06-28
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the stability of Gel'fand inverse spectral problem2005

    • Author(s)
      A. Katsuda
    • Organizer
      Tohoku Geometry Seminar
    • Place of Presentation
      Tohoku Univ
    • Year and Date
      2005-06-28
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] 距離関数のモース理論2005

    • Author(s)
      酒井 隆
    • Organizer
      第3回岡山幾何学談話会
    • Place of Presentation
      岡山理科大学
    • Year and Date
      2005-06-24
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Morse theory of distance functions2005

    • Author(s)
      T. Sakai
    • Organizer
      Okayama Colloquium on Geometry
    • Place of Presentation
      Okayama University of Science
    • Year and Date
      2005-06-24
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the stability of the Gel'fand inverse spectral problem2005

    • Author(s)
      勝田 篤
    • Organizer
      Spectral Analysis, Global Analysis and PDE 2005
    • Place of Presentation
      慶応義塾大学
    • Year and Date
      2005-05-13
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the stability of Gel'fand inverse spectral problem2005

    • Author(s)
      A. Katsuda
    • Organizer
      Spectral Analysis, Global Analysis and PDE 2005
    • Place of Presentation
      Keio Univ
    • Year and Date
      2005-05-13
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] Gel'fandのスペクトル逆問題の安定性について2005

    • Author(s)
      勝田 篤
    • Organizer
      日本数学会年会幾何学分科会特別講演
    • Place of Presentation
      日本大学
    • Year and Date
      2005-03-30
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Presentation] On the stability of Gel'fand inverse spectral problem2005

    • Author(s)
      A. Katsuda
    • Organizer
      Special lecture at annual meeting of Math. Soc. Japan
    • Place of Presentation
      Nihon Univ
    • Year and Date
      2005-03-30
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] EOLSS Encyclopedia of life support system), 6.1.3.4, Differential Geometry2008

    • Author(s)
      T. Sakai
    • Publisher
      Unesco Web(発行予定)
    • Related Report
      2007 Annual Research Report
  • [Book] 解決ボアンカレ予想(数学セミナー増刊号);曲率を調べると位相がわかる2007

    • Author(s)
      酒井 隆(共著)
    • Publisher
      日本評論社
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] 現代幾何学の流れ(砂田利一編):ベルジェ/幾何のエスプリ2007

    • Author(s)
      酒井 隆(共著)
    • Publisher
      日本評論社
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Annual Research Report 2007 Final Research Report Summary
  • [Book] 解決!ポアンカレ予想(数学セミナー増刊)2007

    • Author(s)
      小島定吉, 糸川銚, 酒井隆, 戸田正人, 小林治, 二木昭人, 浦川肇, 十文字正樹, 山口孝男, 塩谷隆, 小林亮一
    • Total Pages
      94
    • Publisher
      日本評論社
    • Related Report
      2006 Annual Research Report
  • [Book] EOLSS(Encyclopedia of life support system), 6.1.3.4, Differential Geometry

    • Author(s)
      T.Sakai
    • Publisher
      Unesco(Web 上発行確定)
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2007 Final Research Report Summary
  • [Book] EOLSS(Encyclopedia of life support system), 6. 1. 3. 4, Differential Geometry

    • Author(s)
      T. Sakai
    • Total Pages
      21
    • Publisher
      Unesco(in a web encyclopedia)(to appear)
    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2007 Final Research Report Summary

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Published: 2005-04-01   Modified: 2016-04-21  

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