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

• Project/Area Number: 21540076
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Nagoya 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: ¥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.

Research Products

• [Journal Article] Lie tensor product manifolds (2012)
  • Author(s): Hajime Sato and Keizo Yamaguchi
  • Journal Title: Demonstratio Mathematica
  • Peer Reviewed
• [Journal Article] Closed planar curves without inflections (2012)
  • Author(s): Shuntaro Ohno, Tetsuya Ozawa and Masaaki Umehara
  • Journal Title: Proc. of the AMS Volume: S0002_9939
  • Peer Reviewed
• [Journal Article] Lie tensor product manifolds (2012)
  • Author(s): Hajime Sato
  • Journal Title: Demonstratio Mathematica Volume: (掲載確定)
  • Peer Reviewed
• [Journal Article] Construction of equivalence maps in Pseudo-Hermitian geometry via linear differ-ential equations (2011)
  • Author(s): Tetsuya Ozawa and Hajime Sato
  • Journal Title: Kodai Math J Volume: 34 Pages: 105-123
  • Peer Reviewed
• [Journal Article] Construction of equivalence maps in pseudo-Hermitian geometry via linear partial differential equations (2011)
  • 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
  • Peer Reviewed
• [Journal Article] 書評 : Contact Geometry and Nonlinear Differential Equations (2009)
  • Author(s): 佐藤肇
  • Journal Title: 数学 61巻 Pages: 326-330
  • 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
• [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
• [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
• [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
• [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
• [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
• [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
• [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
• [Presentation] Contact path geometry, Legendrian webs and Gronwall conjecture (2010)
  • Author(s): Hajime Sato
  • Organizer: Parabolic Geometries and Related Topics
  • Place of Presentation: Tambara Institute of Mathematical Sciences
  • Year and Date: 2010-11-05
• [Presentation] Contact path geometry, Legendrian webs and Gronwall conjecture (2010)
  • 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
• [Presentation] Linearization and Gronwall conjecturef Legendrian webs (2010)
  • Author(s): 佐藤肇
  • Organizer: Geometry and Something
  • Place of Presentation: 福岡大学
  • Year and Date: 2010-10-11
• [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
• [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
• [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
• [Presentation] Lie Tensor Contact Manifolds (2009)
  • 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
• [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
• [Presentation] Geometric structure on the space of singular curves (2009)
  • Author(s): Hajime Sato
  • Organizer: Polish-Japanese Singularity Theory Working Days
  • Place of Presentation: Kazimierz Dolny, Poland
  • Year and Date: 2009-07-14
• [Presentation] Geometric structure on the space of singular curves (2009)
  • Author(s): 佐藤肇
  • Organizer: Polish-Japanese Singularity Theory Working Days
  • Place of Presentation: Kazimierz Dolny(Poland)
  • Year and Date: 2009-07-14
• [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
• [Book] 第3版幾何の魔術 (2012)
  • Author(s): 佐藤肇
  • Publisher: 日本評論社