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Topology of conformally flat Lorentz manifold and various geometric structures

Research Project

Project/Area Number 24540087
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionJosai University (2014)
Tokyo Metropolitan University (2012-2013)

Principal Investigator

KAMISHIMA Yoshinobu  城西大学, 理学部, 教授 (10125304)

Co-Investigator(Kenkyū-buntansha) 長谷川 敬三  新潟大学, 人文社会・教育科学系, 教授 (00208480)
相馬 輝彦  首都大学東京, 理工学研究科, 教授 (50154688)
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords擬リーマン幾何学 / ローレンツ幾何学 / 微分トポロジー / Developing / Holonomy / Uniformization / 平坦 / Lorentz structure / Fefferman metric / Conformally flat / Lightlike vector field / Weyl curvature / Bott tower / infranil manifold / complex contact / lcK structure / Lorentz structure / Seifert fibration / Complex contact / Infrasolv manifold / Holomorphic / Homogeneous
Outline of Final Research Achievements

When the curvature form for the Cartan connection of the parabolic geometry vanishes, a geomeric manifold has a flat structure. The Riemannian flat manifolds have been studied for a long time. In this note we study conformal Lorentz structure as a pseudo-Riemannian structure. If the Weyl conformal curvature tensor vanishes for a Lorentz manifold, it is called a conformally flat Lorentz manifold. We observed that its geometry and topology. We have shown the following results which never show up in Riemannian geometry. (1) If M is a compact complete Lorentzian similarity manifold, then M is a Lorentzian flat space form.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (18 results)

All 2015 2014 2013 2012 Other

All Journal Article (9 results) (of which Peer Reviewed: 8 results) Presentation (9 results) (of which Invited: 7 results)

  • [Journal Article] Homogeneous Locally Conformally Kaehler and Sasaki Manifolds2015

    • Author(s)
      D. Alekseevsky, V. Cortes, K. Hasegawa, Y. Kamishima
    • Journal Title

      International Journal of Mathematics.

      Volume: 近刊

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Locally conformaly Kaehler structures on homogeneous spaces2015

    • Author(s)
      H. Hasegawa and Y. Kamishima
    • Journal Title

      Progress in Mathematics, Birkhuyser

      Volume: 308 Pages: 353-372

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the holomorphic torus-Bott tower of aspherical manifolds2014

    • Author(s)
      Y. Kamishima and M. Nakayama
    • Journal Title

      Proceedings of the Steklov Inst. Math.

      Volume: 286 Pages: 250-264

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Conformally Flat Lorentz Parabolic Manifolds2014

    • Author(s)
      Y. Kamishima
    • Journal Title

      Central European Jour. Math.

      Volume: 12 Pages: 861-878

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Conformally Flat Lorentz Parabolic Manifolds2014

    • Author(s)
      Y.Kamishima
    • Journal Title

      Central European Journal of Mathematics

      Volume: 12 Issue: 6 Pages: 861-878

    • DOI

      10.2478/s11533-013-0379-5

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Locally conformaly Kaehler structures on homogeneous spaces2014

    • Author(s)
      Y. Kamishima and K. Hasegawa
    • Journal Title

      Progress in Math., Birkhauser

      Volume: **

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the holomorphic torus-Bott tower of aspherical manifolds2014

    • Author(s)
      Y. Kamishima and M. Nakayama
    • Journal Title

      The Proceedings of the Steklov Inst. Math.

      Volume: **

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] On Complex Contact Similarity Manifolds2013

    • Author(s)
      Y. kamishima and A. Tanaka
    • Journal Title

      Journal of Mathematics Research

      Volume: 5 Issue: 4 Pages: 1-10

    • DOI

      10.5539/jmr.v5n4p1

    • Related Report
      2013 Research-status Report
  • [Journal Article] Lorentzian similarity manifold2012

    • Author(s)
      Yoshinobu Kamishima
    • Journal Title

      Central European Journal of Mathematics

      Volume: 10 (5) Pages: 1771-1788

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] On the existence of Vaisman lcK structure on locally homogeneous manifolds2014

    • Author(s)
      Y. Kamishima
    • Organizer
      Taipei Workshop on “Analysis and Geometry in Several Complex Variables”
    • Place of Presentation
      台湾, 台北市
    • Year and Date
      2014-12-15 – 2014-12-19
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On complex contact similarity manifoldfs2014

    • Author(s)
      Y. Kamishima
    • Organizer
      The Kortrijk workshop on "Discrete Groups and Geometric Structures, with Applications V”
    • Place of Presentation
      ベルギー, Leuven
    • Year and Date
      2014-06-02 – 2014-06-06
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Conformally flat Lorentzian parabolic manifold)2012

    • Author(s)
      神島芳宣
    • Organizer
      Low-dimensional Geometry and Topology
    • Place of Presentation
      東工大 東京
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Conformally flat Lorentzian parabolic manifold2012

    • Author(s)
      神島芳宣
    • Organizer
      低次元多様体モジュライ空間の幾何学
    • Place of Presentation
      数理解析研究所 京都
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Conformal rigidity on Fefferman-Lorentz manifold and Berman kernal2012

    • Author(s)
      神島芳宣
    • Organizer
      Colloquium, The university of Basilicata
    • Place of Presentation
      Italy Potenza
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] On the holomorphic torus-Bott tower of aspherical manifolds2012

    • Author(s)
      神島芳宣
    • Organizer
      Toric Topology 2012 in Osaka
    • Place of Presentation
      大阪市大  大阪
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Three Geometries on a line2012

    • Author(s)
      神島芳宣
    • Organizer
      Colloquium, Andalas University
    • Place of Presentation
      Padang Indonesia
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] On the holomorphic Torus Bott tower

    • Author(s)
      M. Nakayama and Y. Kamishima
    • Organizer
      Int. conference on Algebraic topology and Abelian functions
    • Place of Presentation
      Steklov Insitutute (Moscow)
    • Related Report
      2013 Research-status Report
  • [Presentation] Nilmanifold上のcomplex contact structure

    • Author(s)
      A. Tanaka and Y. Kamishima
    • Organizer
      日本数学会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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