2009 Fiscal Year Final Research Report
RESEARCH ON THE POISSON GEOMETRY AND THE RELATED GEOMETRIES
| Project/Area Number |
19540065
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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 | Saitama University |
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Principal Investigator |
MIZUTANI Tadayoshi Saitama University, 大学院・理工学研究科, 教授 (20080492)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAMOTO Kunio 埼玉大学, 大学院・理工学研究科, 教授 (70089829)
NAGASE Masayoshi 埼玉大学, 大学院・理工学研究科, 教授 (30175509)
FUKUI Toshizumi 埼玉大学, 大学院・理工学研究科, 教授 (90218892)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 微分トポロジー / ポアソン構造 / 積分可能性 / 包合性 |
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| Research Abstract |
One of the main geometric feature of a Poisson manifold is that its cotangent bundle carries a structure of a Lie algebroid. If a Lie algebroid comes from the normal bundle of the unit space of a Lie groupoid, it is called integrable. All the Lie algebroids are not integrable. Motivated by such integrability problem, we studied the powerful integrability theory (which is the theory of exterior differential systems), along with many geometric applications. As a result, we have acquired fundamental techniques to solve various integrability problems.
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