Research on Contact transformations and Geometric structures of Schwarzian Derivatives
| Project/Area Number |
12640093
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Meijo University |
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Principal Investigator |
OZAWA Tetsuya Meijo University, Faculty of Science and Technology, Department of Mathematics, Professor, 理工学部, 教授 (20169288)
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| Co-Investigator(Kenkyū-buntansha) |
TSUKAMOTO Michirou Meijo University, Faculty of Science and Technology, Department of Mathematics, Lecturer, 理工学部, 講師 (80076637)
KATOU Yoshifumi Meijo University, Faculty of Science and Technology, Department of Mathematics, Assistant Professor, 理工学部, 助教授 (40109278)
OKAMOTO Kiyosato Meijo University, Faculty of Science and Technology, Department of Mathematics, Professor, 理工学部, 教授 (60028115)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2002: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 2001: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 2000: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Schwarzian derivative / Contact manifold / Contact transformation / Conformal Transformation / Conformal Curvatures / Heisenberg Lie Algebra / Infinitesimal transformation / ハイゼンベルグリー環 |
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| Research Abstract |
We established the notion of Schwarzian derivative for contact transformations, that is a generalization of the classical Schwarzian derivative of one complex variable functions. Explicitly, the result is the following:
(1) to obtain the system of partial differential equations to construct contact transformations, which should be called the fundamental equation for the contact geometry,
(2) to obtain a necessary and sufficient condition for the fundamental equations to be integrable,
(3) to verify that the coefficients of the fundamental equation satisfy certain properties as the Schwarzian derivative of the contact transformations.
The method that is developed in the above research was applied to the conformal geometry, and is succeedingly planed to be applied to CR and other geometric structures.
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Report
(4 results)
Research Products
(6 results)
