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Theory of Differential Forms and Twistor Structures

Research Project

Project/Area Number 08454016
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

SATO Hajime  Nagoya Univ., Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (30011612)

Co-Investigator(Kenkyū-buntansha) YAMATO Kazuo  Nagoya Univ., Graduate School of Math, Assoc.Professor, 大学院多元数理科学研究科, 助教授 (30022677)
YASUMOTO Masahiro  Nagoya Univ., Graduate School of Math, Assoc.Professor, 大学院多元数理科学研究科, 助教授 (10144114)
EJIRI Norio  Nagoya Univ., Graduate School of Mathematics, Assoc.Professor, 大学院多元数理科学研究科, 助教授 (80145656)
SHIOTA Masahiro  Nagoya Univ., Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (00027385)
TSUCHIYA Akihito  Nagoya Univ., Graduate School of Mathematics, Professor, 大学院多元数理科学研究科, 教授 (90022673)
向井 茂  名古屋大学, 大学院・多元数理科学研究科, 教授 (80115641)
Project Period (FY) 1996 – 1997
Project Status Completed (Fiscal Year 1997)
Budget Amount *help
¥4,600,000 (Direct Cost: ¥4,600,000)
Fiscal Year 1997: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1996: ¥3,400,000 (Direct Cost: ¥3,400,000)
Keywordsdifferential form / involutive system / twistor / third order ODE / Grassman structure / ツイスター構造
Research Abstract

In this reserch during two years, we have studied the twistor diagram constructed by the head investigator. The diagram gives relations between various geometric structures. We use the theory of involutive system of differential forms and clarified the relations of the diagram with the theory of particles and the field theory. Main purpose of our studies is application of the twistor theory to the classical and quantum mechanics. Especially, we investigated the following geometric strustures in detail : The structure defined by third order ordinary differential equations, projective structures, Grassmann structures, Lie contact structures, etc. We showed that in many cases one equation of a structure is transformed to a simple equation of other geometric structure.
As concrete results, the head investigator with Mrs.A.Y.Yoshikawa studied the equivalence problem under contact diffeomorphism of third order ordinary differential equations, proved that the complete invariants are given by two geometric curvatures and decided the concrete form of the curvatures. By the twistor theory, this result is connected to the geometry of the relativity and gives the fundation of projective contact geometry.Further the head investigator studied the Grassmann structures related to the geometry of the system of second order differential equations and made clear the relation between the half flatness and the twistor theory of the null bundles.

Report

(3 results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • Research Products

    (21 results)

All Other

All Publications (21 results)

  • [Publications] H.Sato: "Third order ordinar differential equation and Legendre connections" J.Math.Soc.Japan. to appear (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Tsuchiya: "The structure of conformal field thory" Suugaku Expositions. 10. 57-92 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 向井 茂: "Brill-Noether理論の非可換化と3次元Fano多様体" 数学. 49. 1-24 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Ejiri: "Degenerate minimal surface of finite total curvature in R^N" Kobe J.Math.14. 11-22 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Izeki: "A deformation of flat conformal strucutures" Trans.Amer.Math.Soc.348. 4939-4964 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 佐藤 肇: "位相幾何(現代数学の基礎2)" 岩波書店, 136 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Sato, A.Y.Yoshikawa: "Third order ordinary differential equation and Legendre connections" J.Math.Soc.Japan. (to appear). (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] A.Tsuchiya: "The structure of conformal field theory" Suugaku Expositions. 10. 57-92 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] S.Mukai: "Non-abelianization of Brill-Noether theory and 3-dimensional Fano manifolds (in Japanese)" Suugaku. 49. 1-24 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] N.Ejiri: "Degenerate minimal surface of finite total curvature in R^N" Kobe J.Math.14. 11-22 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] G.Takeuchi, and M.Yasumoto: "Forcing on bounded arithmetic" Lecture Note in Logic. 6. 120-138 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Izeki: "A deformation of flat conformal structures" Trans.Amer.Math.Soc.348. 4939-4964 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] H.Sato: "Third order ordinar differential equation and Legendre connections" J.Math.Soc.Japan. (to appear). (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] A.Tsuchiya: "The structure of conformal field thory" Suugaku Expositions. 10. 57-92 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 向井茂: "Brill-Noether理論の非可換化と3次元Fano多様体" 数学. 49. 1-24 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] N.Ejiri: "Degenerate minimal surface of finite total curvature in R^N" Kobe J.Math.14. 11-22 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] H.Izeki: "A deformation of flat conformal structures" Trans.Amer.Math.Soc.348. 4939-4964 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] 佐藤 肇: "位相幾何(現代数学の基礎2)" 岩波書店, 136 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] 向井 茂: "単純Lie環とLegender多様体" 名古屋数理フォーラム. 3. 1-12 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 向井 茂: "Brill-Noether理論の悲可換化と3次元Fano多様体" 数学. 49・1. 1-24 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] 佐藤 肇: "位相幾何" 岩波書店, 120 (1996)

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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