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Construction of theory of non-commutative partial differential equations by Schwarzian and twistor methods

Research Project

Project/Area Number 21540076
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

SATO Hajime  名古屋大学, 大学院・多元数理科学研究科, 名誉教授 (30011612)

Co-Investigator(Renkei-kenkyūsha) OZAWA Tetsuya  名城大学, 理工学部, 教授研究者 (20169288)
SUZUKI Hiroshi  名古屋大学, 大学院・多元数理科学研究科, 准教授 (70235993)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsシュワルツ微分 / 放物幾何 / リー構造 / リー・テンソル積構造 / ルジャンドル織物 / グロンウォール予想 / プシュードハーミッシアン構造 / CR多様体 / 田中-ウェブスター接続
Research Abstract

We decide the fundamental system of linear differential equations for pseudo-hermitian structures which are given by fixing a contact form of a CR-manifold. The integrability condition of the system coincides with the vanishing of the torsion and the curvature of the Tanaka-Webster connection. The Lie tensor product structure defined by one root is fundamental element of parabolic geometry. We give the connection of the structure for the basis of the analysis.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (26 results)

All 2012 2011 2010 2009

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (18 results) Book (2 results)

  • [Journal Article] Lie tensor product manifolds2012

    • Author(s)
      Hajime Sato and Keizo Yamaguchi
    • Journal Title

      Demonstratio Mathematica

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Closed planar curves without inflections2012

    • Author(s)
      Shuntaro Ohno, Tetsuya Ozawa and Masaaki Umehara
    • Journal Title

      Proc. of the AMS

      Volume: S0002_9939

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lie tensor product manifolds2012

    • Author(s)
      Hajime Sato
    • Journal Title

      Demonstratio Mathematica

      Volume: (掲載確定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Construction of equivalence maps in Pseudo-Hermitian geometry via linear differ-ential equations2011

    • Author(s)
      Tetsuya Ozawa and Hajime Sato
    • Journal Title

      Kodai Math J

      Volume: 34 Pages: 105-123

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Construction of equivalence maps in pseudo-Hermitian geometry via linear partial differential equations2011

    • Author(s)
      Tetsuya Ozawa
    • Journal Title

      Kodai Mathematical Journal

      Volume: 34 Issue: 1 Pages: 105-123

    • DOI

      10.2996/kmj/1301576765

    • NAID

      130004496128

    • ISSN
      0386-5991, 1881-5472
    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 書評 : Contact Geometry and Nonlinear Differential Equations2009

    • Author(s)
      佐藤肇
    • Journal Title

      数学 61巻

      Pages: 326-330

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 微分式と幾何構造2012

    • Author(s)
      佐藤肇
    • Organizer
      第35回トポロジーセミナー
    • Place of Presentation
      たてやま夕日海岸ホテル
    • Year and Date
      2012-03-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Legendre Webのrank問題2011

    • Author(s)
      佐藤肇
    • Organizer
      複素解析的ベクトル場・葉層構造とその周辺
    • Place of Presentation
      龍谷大学セミナーハウスともいき荘
    • Year and Date
      2011-12-10
    • Related Report
      2011 Final Research Report
  • [Presentation] ジェット束のメタシンプレクティック構造の等方空間2011

    • Author(s)
      佐藤肇
    • Organizer
      シンプレクティック幾何学とその周辺
    • Place of Presentation
      岐阜経済大学
    • Year and Date
      2011-08-25
    • Related Report
      2011 Final Research Report
  • [Presentation] シンプレクティック織物とサミュエルソン条件2011

    • Author(s)
      佐藤肇
    • Organizer
      尾鷲微分トポロジー2011
    • Place of Presentation
      尾鷲中央公民館
    • Year and Date
      2011-08-25
    • Related Report
      2011 Final Research Report
  • [Presentation] 偏微分方程式系の解の特異点2011

    • Author(s)
      佐藤肇
    • Organizer
      特異点論とその応用
    • Place of Presentation
      大分工業高等専門学校
    • Year and Date
      2011-06-01
    • Related Report
      2011 Final Research Report
  • [Presentation] 微分方程式の特性系のはなし2011

    • Author(s)
      佐藤肇
    • Organizer
      接触構造・特異点・微分方程式およびその周辺
    • Place of Presentation
      京都市職員会館かもがわ
    • Year and Date
      2011-01-22
    • Related Report
      2011 Final Research Report
  • [Presentation] Web, NomographとGronwall予想2010

    • Author(s)
      佐藤肇
    • Organizer
      複素解析的ベクトル場・葉層構造とその周辺
    • Place of Presentation
      龍谷大学セミナーハウスともいき荘
    • Year and Date
      2010-11-26
    • Related Report
      2011 Final Research Report
  • [Presentation] ラグランジュ織物とルジャンドル織物2010

    • Author(s)
      佐藤肇
    • Organizer
      シンプレクティック幾何学とその周辺
    • Place of Presentation
      放送大学秋田学習センター
    • Year and Date
      2010-11-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Contact path geometry, Legendrian webs and Gronwall conjecture2010

    • Author(s)
      Hajime Sato
    • Organizer
      Parabolic Geometries and Related Topics
    • Place of Presentation
      Tambara Institute of Mathematical Sciences
    • Year and Date
      2010-11-05
    • Related Report
      2011 Final Research Report
  • [Presentation] Contact path geometry, Legendrian webs and Gronwall conjecture2010

    • Author(s)
      佐藤肇
    • Organizer
      Parabolic Geometries and Related Topics
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県)
    • Year and Date
      2010-11-05
    • Related Report
      2010 Annual Research Report
  • [Presentation] Linearization and Gronwall conjecturef Legendrian webs2010

    • Author(s)
      佐藤肇
    • Organizer
      Geometry and Something
    • Place of Presentation
      福岡大学
    • Year and Date
      2010-10-11
    • Related Report
      2011 Final Research Report
  • [Presentation] Legendre WebとGronwall予想2010

    • Author(s)
      佐藤肇
    • Organizer
      広島幾何学研究集会2010
    • Place of Presentation
      広島大学
    • Year and Date
      2010-10-07
    • Related Report
      2011 Final Research Report
  • [Presentation] Legendreウェッブと効用理論2010

    • Author(s)
      佐藤肇
    • Organizer
      尾鷲微分トポロジー2010
    • Place of Presentation
      尾鷲中央公民館
    • Year and Date
      2010-08-26
    • Related Report
      2011 Final Research Report
  • [Presentation] 3次元擬エルミート構造の基本微分方程式2010

    • Author(s)
      佐藤肇
    • Organizer
      接触構造・特異点・微分方程式およびその周辺
    • Place of Presentation
      洞爺湖文化センター
    • Year and Date
      2010-01-28
    • Related Report
      2011 Final Research Report
  • [Presentation] Lie Tensor Contact Manifolds2009

    • Author(s)
      佐藤肇
    • Organizer
      Symplectic Geometryとその周辺
    • Place of Presentation
      岐阜経済大学
    • Year and Date
      2009-11-25
    • Related Report
      2011 Final Research Report
  • [Presentation] 手術理論などの初期の微分位相幾何と微分同相群の非有限性2009

    • Author(s)
      佐藤肇
    • Organizer
      山代微分トポロジー
    • Place of Presentation
      山代地区会館
    • Year and Date
      2009-08-21
    • Related Report
      2011 Final Research Report
  • [Presentation] Geometric structure on the space of singular curves2009

    • Author(s)
      Hajime Sato
    • Organizer
      Polish-Japanese Singularity Theory Working Days
    • Place of Presentation
      Kazimierz Dolny, Poland
    • Year and Date
      2009-07-14
    • Related Report
      2011 Final Research Report
  • [Presentation] Geometric structure on the space of singular curves2009

    • Author(s)
      佐藤肇
    • Organizer
      Polish-Japanese Singularity Theory Working Days
    • Place of Presentation
      Kazimierz Dolny(Poland)
    • Year and Date
      2009-07-14
    • Related Report
      2009 Annual Research Report
  • [Book] 第3版幾何の魔術2012

    • Author(s)
      佐藤肇・一楽重雄
    • Total Pages
      156
    • Publisher
      日本評論社
    • Related Report
      2011 Final Research Report
  • [Book] 第3版幾何の魔術2012

    • Author(s)
      佐藤肇
    • Publisher
      日本評論社
    • Related Report
      2011 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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