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Geometric Structures and Manifold Structures

Research Project

Project/Area Number 01302002
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionOkayama University

Principal Investigator

SAKAI Takashi  Okayama U., Fac. Sci., Professor, 理学部, 教授 (70005809)

Co-Investigator(Kenkyū-buntansha) OHNITA Yoshihiro  Tokyo Metro. U., Fac. Sci., Assistant, 理学部, 助手 (90183764)
KASUE Atushi  Osaka U., Fac. Sci., Associate Prof., 理学部, 助教授 (40152657)
NISHIKAWA Seiki  Tohoku U., Fac. Sci., Associate Prof., 理学部, 助教授 (60004488)
SATO Hajime  Nagoya U., Col. of Gen. Ed., Professor, 教養部, 教授 (30011612)
TANNO Shukichi  Tokyo Inst. Tech., Fac. Sci., Professor, 理学部, 教授 (10004293)
市田 良輔  横浜市立大学, 文理学部, 助教授 (10094294)
Project Period (FY) 1989 – 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1990: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1989: ¥1,300,000 (Direct Cost: ¥1,300,000)
KeywordsGeometric Structure / Manifold Structures / Curvature and Topology
Research Abstract

The purpose of the present research project is to investigate collectively various properties of geometric structures on manifolds and their relations to the manifold structures, in the cooperation of many geometers in Japan.
As for the metric structures, T.Sakai considered the inequalities which hold between metric invariants with respect to measure and get results on the isosystolic inequality and isodiametric inequality for compact surfaces. Now series of Gromov's outstanding works are having a great influence upon the study on the relation between the metric structures and the manifold structures. A. Kasue gave a proof of Gromov's convergence theorem and applied it to the study of the structure of manifolds of asymptotically non-negative curvature. He also constructed the coordinates at infinity of ALE-menifolds under some geometric condition with S.Bando and H. Nakajima. K. Fukaya and T.Yamaguchi get decisive results on the structure of almost non-positive and almost non-negative c … More urvature using excellent techniques extending Gromov's ideas.
As for the other geometric structures, the study of contact metric structures was initiated and has been done mainly in Japan. S. Tanno gave a characterization of the canonical contact metric structures associated with the contact form from the variational view point. H.Sato proposed to study Lie's sphere geometry from the view point of G-structure and applied Tanaka's theory with K. Yamaguchi.
On the other hand, one of the main trends of the recent progress on the study of geometric structures, for examples the study of minimal surfaces and harmonic mappings, has been made by applying new techniques from the analysis. S. Nishiwaka applied the heat equation method to the study of geometric foliations on the manifolds. As for harmonic mappings we have the researches by A. Kasue, H. Naito and others from the analytic view point and the researches by Y. Ohnita and others from the geometric view point.
Now under the present Grant-in-aid for scientific research, we organized the following symposiums: "Surveys in Geometry - Minimal surfaces" (Univ. of Tokyo), "Variational problems appearing in geometry" (International Center of Osaka City Univ.), "Geometric structures and manifold structures" (Okayama niv.). We distributed printed research materials to the participants and had active and fruitful discussions. Less

Report

(3 results)
  • 1990 Annual Research Report   Final Research Report Summary
  • 1989 Annual Research Report
  • Research Products

    (28 results)

All Other

All Publications (28 results)

  • [Publications] SAKAI,T: "On levels of the distance function from the boundary of convex domain" Preprint,1990.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] SAKAI,T.(with R.NODA and M.MORIMOTO): "Generalized Fermat's problem" Canadian J.Math.,to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] TANNO,S: "The Bochner type curvature tensor of contact Riemannian structure" Hokkaido Math.J.19. 55-66 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] NISHIKAWA,S.(with M.RAMACHANDRAN, P.TONDEUR): "The heat equation for Riemannian foliation" Trans.Amer.Math.Soc.319. 119-130 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] KASUE,A.(with T.WASHIO): "Growtu of equivariant harmonic maps and harmonic morphisms" Osaka J.Math.27. 899-928 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] OHNITA,Y.(with G.VALLI): "Pluriharmonic maps into compact Lie groups and factorization into unitons" Proc.London Mach.Soc.,to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 酒井 隆: "リ-マン幾何学" 裳華房, (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] SAKAI, T: "On levels of the distance function from the boundary of convex domain" Preprint. (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] SAKAI, T. (With R. NODA and M. MORIMOTO): "Generalized Fermat's problem," Canadian J. Math.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] TANNO, S.: "The Bochner type curvature tensor of contact Riemannian structure" Hokkaido Math. J.19. 55-66 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] NISHIKAWA, S. (With M. RAMACHANDRAN and P. TONDEUR): "The heat equation for Riemannian foliations" Trans. Amer. Math. Soc.319. 119-130 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] KASUE, A. (With T. WASHIO): "Growth of equivariant harmonic maps and harmonic morphisms" Osaka J. Math.27. 899-928 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] OHNITA, Y. (With G. VALLI): "Pluriharmonic maps into compact Lie groups and factorization into unitons" Proc. London Math. Soc.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] SAKAI, T.: Shokabo. Riemannian Geometry (in Japanese),

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] SAKAI,T: "On levels of the distance function from the boundary of convex domain"

    • Related Report
      1990 Annual Research Report
  • [Publications] SAKAI,T.(with R.NODA and M.MORIMOTO): "Generalized Fermat's problem" Canadian J.Math.,.

    • Related Report
      1990 Annual Research Report
  • [Publications] TANNO,S: "The Bochner type curvature tensor of contact Riemannian structure" Hokkaido Math.J.19. 55-66 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] NISHIKAWA,S.(with M.RAMACHANDRAN,P.TONDEUR): "The heat equation for Riemannian foliation" Trans.Amer.Math.Soc.319. 119-130 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] KASUE,A.(with T.WASHIO): "Growth of equivariant harmonic maps and harmonic morphisms" Osaka J.Math.27. 899-928 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] OHNITA,Y.(with G.VALLI): "Pluriharmonic maps into compact Lie groups and factorization into unitons" Proc.London Math.Soc.,.

    • Related Report
      1990 Annual Research Report
  • [Publications] 酒井 隆: "リ-マン幾何学" 裳華房, (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Takashi SAKAI: "On the isodiametric inequality for the 2-sphere" Geometry of Manifolds(edited by K.Shiohama)Perspectives in Math.(Academic Press). 8. 303-316 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Takashi SAKAI(with R.NODA and M.MORIMOTO): "Generalized Fermat's problem" Canadian Math.J.,to appear.

    • Related Report
      1989 Annual Research Report
  • [Publications] Hajime SATO(with K.YAMAGUCHI): "Lie contact manifolds" Geometry of Manifolds(edited by K.Shiohama)Perspectives in Math.(Academic Press). 8. 191-238 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Seiki NISHIKAWA(with P.TONDEUR): "Transversal infinitesimal automorphisms of harmonic foliations on complete manifolds" Ann.Global Anal.Geom.7. 44-57 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Ryosuke ICHIDA: "On decompositions of Riemannian manifolds with nonnegative Ricci curvature" Geometry of Manifolds(edited by K.Shiohama)Perspectives in Math.(Academic Press). 8. 247-274 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Atsushi KASUE: "A convergence theorem for Riemannian manifolds and some applications" Nagoya Math.J.114. 21-51 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 酒井隆: "リ-マン幾何" 裳華房, (1990)

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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