2000 Fiscal Year Final Research Report Summary
Geometry of webs, Hamiltonian systems and complex dynamics
| Project/Area Number |
10440014
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| Research Category |
Grant-in-Aid for Scientific Research (B).
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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 | Ochanomizu University (1999-2000)
Hokkaido University (1998) |
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Principal Investigator |
NAKAI Isao Ochanomizu University, Faculty of Science, Professor, 理学部, 教授 (90207704)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Hajime Nagoya University, Graduate School of Mathematics, Profe, 大学院・多元数理科学研究科, 教授 (30011612)
YOSHINO Masatomi Chuo University, Faculty of Economics, Professor, 経済学部, 教授 (00145658)
SUWA Tatsuo Hokkaido University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40109418)
MATSUMOTO Shigenori Nihon University, College of Science and Technology, Professor, 理工学部, 教授 (80060143)
KIKKAWA Michihika Shimane University, President, 学長 (70032430)
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| Project Period (FY) |
1998 – 2000
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| Keywords | WEB / Foliation / Complex dynamics / Quasi group / Caustics / Chern connection / difraction / co-tidal |
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| Research Abstract |
We defined a canonical affine connection for integrable first order partial differential equations of finite type, and investigated its singularities along the locus where the foliation structure of solutions degenerates. We proved there exists one to one correspondence of the moduli space of equations and the space of curvature forms in some cases. We proved also the triangulability of the mapping cylinder of generic smooth mappings of manifolds. As an application we proved a naturality formula of the stiefel-homology functor of constructible functions on manifolds to homology classes.
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