Study on relations between differential equations and geometric structures by the method of twistor theory

• Project/Area Number: 22540109
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Numazu National College of Technology
• Principal Investigator: MACHIDA YOSHINORI 沼津工業高等専門学校, 教養科, 教授 (90141895)
• Co-Investigator(Renkei-kenkyūsha): ISHIKAWA Goo 北海道大学, 理学研究科, 教授 (50176161) ; MORIMOTO Tohru 奈良女子大学, 名誉教授 (80025460) ; FUJII Kazuyuki 横浜市立大学, 総合科学部, 教授 (00128084) ; TAKAHASHI Masatomo 室蘭工業大学, ひと文化系, 准教授 (80431302)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: ツイスター理論 / 微分方程式 / 幾何構造 / 旗多様体 / D_4図式 / 共形３対性 / 超幾何積分 / ガウス・マニン接続 / 次数つきリー代数表現 / 線形微分方程式系 / 外在的幾何 / D_4型旗多様体 / 共形3対性 / 重みつき微分方程式 / コーン場 / ラグランジュ・グラスマン射影双対 / リー代数表現 / 終結式 / モンジュ・アンペール系 / 非ガウス型積分 / モンジュ・アンペール方程式

Research Abstract

An observation of twistor theory is to research relations and correspondences between different geometric structures via double fibrations. For various classes of differential equations associated with geometric structures, we study geometric meanings of equations, properties of solutions, constructions of equations and solutions. We discuss differential equations associated with cone structures, Monge-Ampere systems, equations associated with Lie algebra representations, equations associated with integrals of powers of polynomials. Treating with conformal triality from D_4 twistor diagram, we study the geometric structures, singularities, and differential equations. Treating with Kaluza-Klein space-time with (3,3) type, we study the scalar field, the vector field, the spinor field induced by the conformal SO(4,4) representation.

Research Products

• [Journal Article] Double filtration of twisted logarithmic complex and Gauss-Manin connection (2014)
  • Author(s): 待田芳徳、青本和彦
  • Journal Title: J. Math. Soc. Japan Volume: JMSJ6590
  • NAID: 130005069892
  • Peer Reviewed
• [Journal Article] Geometry of D_4 conformal triality and sibgularities of tangent surfaces (2014)
  • Author(s): 待田芳徳、石川剛郎、高橋雅朋
  • Journal Title: Hokkaido Univ. EPrints Server Volume: 1051 Pages: 1-25
• [Journal Article] Singularities of tangent surfaces in Caetan's split G_2-geometry (2012)
  • Author(s): 待田芳徳、石川剛郎、高橋雅朋
  • Journal Title: Hokkaido Univ. EPrints Server Volume: 1020 Pages: 1-26
• [Journal Article] Asymmetry in singularities of tangent surfaces in contact-cone Legendre-null duality (2011)
  • Author(s): 待田芳徳、石川剛郎、高橋雅朋
  • Journal Title: J. Singularities Volume: 3 Pages: 126-143
  • Peer Reviewed
• [Journal Article] Asymmetry in singularities of tangent surfaces in contact-cone Legendrenull duality (2011)
  • Author(s): 待田芳徳, 石川剛郎, 高橋雅朋
  • Journal Title: Journal of Singularities Volume: 3 Pages: 126-143
  • Peer Reviewed
• [Presentation] D_4図式からの共形3対性の幾何と特異点 (2013)
  • Author(s): 待田芳徳
  • Organizer: 日本数学会・秋季総合分科会
  • Place of Presentation: 愛媛大学
  • Year and Date: 2013-09-24
• [Presentation] Gauss-Manin connections derived from one-dimensional hypergeometric integrals (2013)
  • Author(s): 待田芳徳
  • Organizer: Singularities in geometry and applications III
  • Place of Presentation: イギリス・エジンバラ
  • Year and Date: 2013-09-04
• [Presentation] 射影双対性から共形3対性 (2012)
  • Author(s): 待田芳徳
  • Organizer: シンプレクティック幾何とその周辺
  • Place of Presentation: 秋田大学
  • Year and Date: 2012-11-20
• [Presentation] 判別式と終結式に関連する微分方程式 (2011)
  • Author(s): 待田芳徳
  • Organizer: シンプレクティック幾何とその周辺
  • Place of Presentation: 岐阜経済大学
  • Year and Date: 2011-11-10
• [Presentation] リー代数の表現に付随した微分方程式 (2010)
  • Author(s): 待田芳徳
  • Organizer: リー群とその周辺
  • Place of Presentation: 信州大学
  • Year and Date: 2010-10-10
• [Presentation] Monge-Ampere systems with Lagrange pairs (2010)
  • Author(s): 待田芳徳
  • Organizer: 11^<th> international and its applications
  • Place of Presentation: チェコ・ブルノ
  • Year and Date: 2010-08-29
• [Presentation] D_4図式からの共形３対性の幾何と特異点
  • Author(s): 待田 芳徳
  • Organizer: 日本数学会・秋季総合分科会
  • Place of Presentation: 愛媛大学
• [Book] 数理の玉手箱 (2010)
  • Author(s): 待田芳徳、藤井一幸、鈴木達夫、浅田明、岩井敏洋
  • Publisher: 遊星社
• [Book] 数理の玉手箱 (2010)
  • Author(s): 藤井, 鈴木, 浅田, 待田, 岩井共著
  • Total Pages: 205
  • Publisher: 遊星社