2002 Fiscal Year Final Research Report Summary
Studies on Poissonization of Nambu-Jacobi structures
| Project/Area Number |
13640058
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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 | Akita University |
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Principal Investigator |
MIKAMI Kentaro Akita Univ. Fac. ERS., Prof., 工学資源学部, 教授 (70006592)
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| Co-Investigator(Kenkyū-buntansha) |
KOBAYASHI Mahito Akita U. Fac. ERS., Ass. Prof., 工学資源学部, 助教授 (10261645)
KAWAKAMI Hajime Akita U. Fac. ERS., Ass. Prof., 工学資源学部, 助教授 (20240781)
TATEOKA Atsushi Akita U. Fac. EHS., Prof., 教育文化学部, 教授 (40006565)
TORISU Ichiro Akita U. Fac. ERS., Assistant, 工学資源学部, 助手 (50323134)
UNO Chikara Akita U. Fac. EHS., Ass. Prof., 教育文化学部, 助教授 (20282155)
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| Project Period (FY) |
2001 – 2002
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| Keywords | symplectic structure / Poisson structure / Nambu-Jacobi structure / tangent distribution / contact structure / Engel structure / Lie algebroid |
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| Research Abstract |
In the first year (Heisei 13), as a first step of studying of Poissonization of Nambu-Jacobi structures, we handled tangent distributions whose co-rank are no less than 2 and studies about relations between their annihilator sub-bundles and geometric properties of them. When co-dimension is 2, the dimension of manifold should be even and we checked that Engel manifolds are one of those examples. On the other hand, it turned out any 2-dimensional non-involutive distribution has this property and higher dimensional cases are still left unsolved for us.
In the second year (Heisei 14), we have payed attention to tangent distributions generated by 2-vector field. We found a Lie algebroid which looks brand-new. We asked A. Weinstein (Univ. of California, Berkeley) and I. Vaisman (Univ. of Haifa) about our result and got reply that they think our result is new and original. We are writing this research as a tentative title "Integrability of plane fields defined by 2-vector fields" as a joint-work with Professor T. Mizutani at Saitama Univ.
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