| Project/Area Number |
23540081
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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 | Kanazawa University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MORIYA Katsuhiro 筑波大学, 数理物質科学研究科(系), 助教 (50322011)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUKADA Kazumi お茶の水女子大学, 人間文化創成科学研究科, 教授 (30163760)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | ツイスターリフト / ツイスター空間 / 四元数多様体 / 四元数正則構造 / 調和切断 |
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| Outline of Final Research Achievements |
We find some invariants which are independent of the choice of connections preserving the quaternion structure. We study the relations among those invariants and extrinsic quantities for submanifolds, in particular, topological ones. As an application, an inequality for the Euler number of the normal bundle of a twistor holomorphic surface, which is given by T. Friedrich, can be improved. We also study submanifolds in quaternion Kaehler manifolds whose twistor lifts are harmonic sections. As a special case, we see that the twistor lift of a twistor holomorphic surface in a quaternion Kaehler manifold is a harmonic section. It is a generalization of a Leschke's result.
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