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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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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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 / 外微分形式系 / G構造 / 接触変換 / 延長 / ウェッブ構造 / スペンサーコホモロジー / 描板 / 接触多様体 / Lie亜代数 / ボアソン幾何学 / 包合系 / オイラー・ラグランジュ方程式 / 接触構造 / モンジュ・アンペール方程式 |
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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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Report
(4 results)
Research Products
(11 results)
