2003 Fiscal Year Final Research Report Summary
Geometry of Partial Differential Equation, Spin Structure and Twistor Theory
| Project/Area Number |
12304004
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Nagoya University |
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Principal Investigator |
SATO Hajime Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (30011612)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Ryoichi Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (20162034)
NAMIKAWA Yukihiro Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (20022676)
TSHUCHIYA Akihiro Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (90022673)
OHTA Hiroshi Nagoya University, Graduate School of Mathematics, Assoc.Prof., 大学院・多元数理科学研究科, 助教授 (50223839)
NAYATANI Shin Nagoya University, Graduate School of Mathematics, Assoc.Prof., 大学院・多元数理科学研究科, 助教授 (70222180)
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| Project Period (FY) |
2000 – 2003
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| Keywords | PDE / Twistor thory / Grassmannian structure / Projective contact / Lagrangean / 3^<rd> order ODE |
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| Research Abstract |
As concrete examples of geometric structures related to system of geometric equations, we investigated the following pair structures by using the twistor correspondence.
a) projective and Grassmannian b) projective contact and Lagrangean c) Lie contact and Lorentzian d) pure spinor and neutral structures
We studied in detail the structures, got invariants and classified them. Further we extended the investigations to many different directions.
As for a), the head investigator and Machida worked together to obtain complete invariants as elements of Spencer cohomology.
Concerning b), the joint work of the head and Yoshikawa was the starting point of the investigation. Ozawa and the head found a system of partial differential equations, which gives a concrete contact transformation.
As for c) and d), we got the twistor diagrams and the relation of invariants. As a new extension of the study of differential equations, we got a fundamental system for the conformal structure, which may have many applications in geometry.
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