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RESEARCH ON THE POISSON GEOMETRY AND THE RELATED GEOMETRIES

Research Project

Project/Area Number 19540065
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionSaitama University

Principal Investigator

MIZUTANI Tadayoshi  Saitama University, 大学院・理工学研究科, 教授 (20080492)

Co-Investigator(Kenkyū-buntansha) SAKAMOTO Kunio  埼玉大学, 大学院・理工学研究科, 教授 (70089829)
NAGASE Masayoshi  埼玉大学, 大学院・理工学研究科, 教授 (30175509)
FUKUI Toshizumi  埼玉大学, 大学院・理工学研究科, 教授 (90218892)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords微分トポロジー / ポアソン構造 / 積分可能性 / 包合性 / 外微分形式系 / G構造 / 接触変換 / 延長 / ウェッブ構造 / スペンサーコホモロジー / 描板 / 接触多様体 / Lie亜代数 / ボアソン幾何学 / 包合系 / オイラー・ラグランジュ方程式 / 接触構造 / モンジュ・アンペール方程式
Research Abstract

One of the main geometric feature of a Poisson manifold is that its cotangent bundle carries a structure of a Lie algebroid. If a Lie algebroid comes from the normal bundle of the unit space of a Lie groupoid, it is called integrable. All the Lie algebroids are not integrable. Motivated by such integrability problem, we studied the powerful integrability theory (which is the theory of exterior differential systems), along with many geometric applications. As a result, we have acquired fundamental techniques to solve various integrability problems.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (12 results)

All 2010 2009 2008 2007 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (4 results) Remarks (1 results)

  • [Journal Article] Tame nonsmooth inverse mapping theorems2010

    • Author(s)
      T. Fukui, K. Kurdyka, L. Paunescu
    • Journal Title

      SIAM J.Optim. Vol. 20

      Pages: 1573-1590

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tame nonsmooth inverse mapping theorems2010

    • Author(s)
      Toshizumi Fukui
    • Journal Title

      SIAM J.Optim. 20巻

      Pages: 1573-1590

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Laplacian and the heat kernel acting on differential forms on spheres2009

    • Author(s)
      Masayoshi Nagase
    • Journal Title

      Tohoku Math.Journal Vol. 61

      Pages: 571-588

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Laplacian and the heat kernel acting on differential forms on spheres2009

    • Author(s)
      Masayoshi Nagase
    • Journal Title

      Tohoku Math.Journal 61巻

      Pages: 571-588

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Twistor spaces and the general adiabatic expansions2007

    • Author(s)
      Masayoshi Nagase
    • Journal Title

      J.Funct.Anal. Vol. 251

      Pages: 680-737

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Algebroids Associated with Pre-Poisson Structures ; noncommutative geometry and physics 20052007

    • Author(s)
      Kentaro Mikami, Tadayoshi Mizutani
    • Journal Title

      Proceedings of the International Sendai-Beijing Joint Workshop, (World Scientific)

      Pages: 71-96

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Twistor spaces and the general adiabatic expansions2007

    • Author(s)
      Masayoshi Nagase
    • Journal Title

      J.Funct.AnaL 251

      Pages: 680-737

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] 描板とスペンサーコホロジーについて2009

    • Author(s)
      水谷忠良
    • Organizer
      東工大土曜セミナー
    • Place of Presentation
      東京工業大学
    • Year and Date
      2009-02-21
    • Related Report
      2009 Final Research Report
  • [Presentation] 描板とスペンサーコホモロジーについて2009

    • Author(s)
      水谷忠良
    • Organizer
      東工大土曜セミナー
    • Place of Presentation
      東京工業大学
    • Year and Date
      2009-02-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] G構造の構造関数について2008

    • Author(s)
      水谷忠良
    • Organizer
      東工大土曜セミナー
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-06-21
    • Related Report
      2009 Final Research Report 2008 Annual Research Report
  • [Presentation] 接触多様体上の Euler-Lagrange 外微分形式系と Noether の定理について2007

    • Author(s)
      水谷忠良
    • Organizer
      量子化の幾何学2007
    • Place of Presentation
      早稲田大学
    • Year and Date
      2007-09-07
    • Related Report
      2009 Final Research Report
  • [Remarks] ホームページ等

    • Related Report
      2009 Final Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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