Flexibility of Reeb flows in contact manifolds
| Project/Area Number |
15K04837
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Chiba University |
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Principal Investigator |
Inaba Takashi 千葉大学, 大学院理学研究院, 名誉教授 (40125901)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUBOI Takashi 東京大学, 大学院数理科学研究科, 教授 (40114566)
MATSUMOTO Shigenori 日本大学, 理工学部, 名誉教授 (30186374)
MITSUMATSU Yoshihiko 中央大学, 理工学部, 教授 (90206441)
NAKAYAMA Hiromichi 青山学院大学, 理工学部, 教授 (30227970)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | レーブ流 / 接触構造 / Reeb流 / contact Hamiltonian 関数 / 不変集合 |
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| Outline of Final Research Achievements |
We have studied a method of modifying a Reeb flow by changing a contact form while keeping a contact structure unchanged. We have realized, in a Darboux chart, products of spheres as an invariant set of a Reeb flow. We have also proved the following extension theorem for Reeb flows. Let (M,D) be a compact contact manifold, N a submanifold of M and φ a flow on N. Then, φ extends to a Reeb flow on M if and only if φ preserves the intersection of D and TN. Moreover, if N is isotropic, then, any flow on N transverse to D extends, after a suitable reparametrization, to a Reeb flow.
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Report
(4 results)
Research Products
(6 results)
