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2010 Fiscal Year Final Research Report

Geometric structure on geometric manifolds which admit Lie group transformations and various Rigidity

Research Project

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Project/Area Number 20340013
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTokyo Metropolitan University

Principal Investigator

KAMISHIMA Yoshinobu  Tokyo Metropolitan University, 大学院・理工学研究科, 教授 (10125304)

Co-Investigator(Kenkyū-buntansha) MARTIN GUEST  首都大学東京, 大学院・理工学研究科, 教授 (10295470)
SOMA Teruhiko  首都大学東京, 大学院・理工学研究科, 教授 (50154688)
IMAI Jun  首都大学東京, 大学院・理工学研究科, 准教授 (70221132)
KAMIYA Shigeyasu  岡山理科大学, 工学部, 教授 (80122381)
HASEGAWA Keizo  新潟大学, 人文社会・教育系, 教授 (00208480)
Co-Investigator(Renkei-kenkyūsha) SAKAI Takashi  首都大学東京, 大学院・理工学研究科, 助教 (30381445)
Project Period (FY) 2008 – 2010
Keywords幾何学 / 微分幾何学 / 微分トポロジー
Research Abstract

We have examined the following projects.
(1) Approach from geometry and topology concerning conformally Fefferman-Lorentz manifolds.
(1) We proved the analogue of the Obata-Ferrand theorem to Lorentz manifolds.
(2) We proved the Kuiper's problem that if the developing map is not surjective on the universal cover of S^<n-1,1>, then it is a covering map onto its image under the existence of causal vector fields.
(2) We studied the infrasolv-fiber space structure and the smooth rigidity on the closed aspherical manifolds of the mixed type. As an application, we proved the smooth rigidity of compact aspherical homogeneous manifolds.

  • Research Products

    (21 results)

All 2010 2009 2008 2007

All Journal Article (15 results) Presentation (6 results)

  • [Journal Article] Nondegenerate conformal, CR, Quaternionic CR structure on Manifolds2010

    • Author(s)
      神島芳宣
    • Journal Title

      Handbook of Pseudo-Riemannian Geometry and Supersymmetry, (ed. Vicente Cortes) Vol.16

      Pages: 863-896

  • [Journal Article] Pseudoharmonic maps and vector fields on CR manifolds2010

    • Author(s)
      神島芳宣, Sorin Dragomir
    • Journal Title

      Jour.Math.Soc.Japan Vol.62

      Pages: 269-303

  • [Journal Article] Coexistence of invariant sets with and without SRB measures in Henon family2010

    • Author(s)
      相馬輝彦, S. Kiriki
    • Journal Title

      Nonlinearity Vol.23

      Pages: 2253-2269

  • [Journal Article] Differential equations aspects of quantum cohomology2010

    • Author(s)
      Martin Guest
    • Journal Title

      in : Geometric and Topological Methods for Quantum Field Theory(Cambridge Univ. Press) Vol.501

      Pages: 54-85

  • [Journal Article] Small deformations and non-left-invariant complex structures on six-dimensional compact solvmanifolds2010

    • Author(s)
      長谷川敬三
    • Journal Title

      Differential Geom.Appl. Vol.28

      Pages: 220-227

  • [Journal Article] Seifert fibred structure and rigidity on real Bott towers2009

    • Author(s)
      神島芳宣, Admi Nazra
    • Journal Title

      Contemp.Math.of A.M.S. Vol.501

      Pages: 103-122

  • [Journal Article] Cohomological Rigidity of real Bott manifolds2009

    • Author(s)
      神島芳宣, Mikiya Masuda
    • Journal Title

      Algebraic Topology and Geometry Vol.9

      Pages: 2479-2502

  • [Journal Article] On the limits sets of spherical CR manifolds2009

    • Author(s)
      神島芳宣, Omolola Odebiyi
    • Journal Title

      Bulletin of Institute of Mathematics, Academia Sinica, New Series Vol.4

      Pages: 189-217

  • [Journal Article] Complex and Kahler structures on compact homogeneous manifolds-their existence, classification and moduli problem2009

    • Author(s)
      長谷川敬三
    • Journal Title

      Adv.Stud.Pure Math., 56, Math.Soc.Japan, Tokyo Vol.56,

      Pages: 151-167

  • [Journal Article] Pseudo-conformal quaternionic, CR structure on (4n+3)-dimensional manifolds2008

    • Author(s)
      神島芳宣, Dmitri Alekseevsky
    • Journal Title

      Annali di Matematica Pura ed Applicata Vol.187

      Pages: 487-529

  • [Journal Article] Persistent antimonotonic bifurcations and strange attractors for cubic homoclinic tangencies2008

    • Author(s)
      相馬輝彦, S. Kiriki
    • Journal Title

      Nonlinearity Vol.21

      Pages: 1105-1140

  • [Journal Article] From Quantum Cohomology to Integrable Systems2008

    • Author(s)
      Martin Guest
    • Journal Title

      Oxford University Press Vol.501

      Pages: 305

  • [Journal Article] Discrete subgroups of PU (2, 1) with screw parabolic elements2008

    • Author(s)
      神谷茂保, J. Parker
    • Journal Title

      Math.Proc.Cambridge Philos.Soc. Vol.144

      Pages: 443-455

  • [Journal Article] Energy of knots and the infinitesimal cross ratio, Proceedings of the Conference Groups2008

    • Author(s)
      今井淳
    • Journal Title

      Homotopy and Configuration Spaces, Geometry and Topology Monographs Vol.13

      Pages: 421-445

  • [Journal Article] The configuration space of planar spidery linkages2007

    • Author(s)
      今井淳
    • Journal Title

      Topology Appl. Vol.154

      Pages: 502-526

  • [Presentation] Conformally flat Fefferman-Lorentz manifold and Obata and Ferrand Rigidity2010

    • Author(s)
      神島芳宣
    • Organizer
      研究集会「擬リーマン幾何学とその関連する話題」
    • Place of Presentation
      お茶の水女子大学東京 講演
    • Year and Date
      20101200
  • [Presentation] Conformally flat Fefferman-Lorentz manifolds2010

    • Author(s)
      神島芳宣
    • Organizer
      Workshop in Flat conformal Lorentzian structures
    • Place of Presentation
      Princeton University, Princeton, US. 講演
    • Year and Date
      20101200
  • [Presentation] Conformally Lorentz parabolic structure and Fefferman-Lorentz metric2010

    • Author(s)
      神島芳宣
    • Organizer
      Workshop in Parabolic geometry and related topics
    • Place of Presentation
      Tambara Seminar House(玉原)群馬県 講演
    • Year and Date
      20101100
  • [Presentation] Conformal flow on compact Lorentz manifolds and Obata-Ferrand's theorem and Fefferman metrics2008

    • Author(s)
      神島芳宣
    • Organizer
      第35回変換群シンポジウム
    • Place of Presentation
      岡山 講演
    • Year and Date
      20081100
  • [Presentation] Conformal flow on Lorentz manifolds2008

    • Author(s)
      神島芳宣
    • Organizer
      科学技術院(Korea Advanced Institute of Science and Technology), 研究集会
    • Place of Presentation
      大田(韓国) 講演
    • Year and Date
      20080800
  • [Presentation] Seifert structures on real Bott towers2008

    • Author(s)
      神島芳宣
    • Organizer
      Conference on Discrete Groups and Geometric Structures, with Applications III, K.U.Leuven Campus
    • Place of Presentation
      Kortrijk, Belgium 講演
    • Year and Date
      20080500

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Published: 2012-01-26   Modified: 2018-02-02  

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