2016 Fiscal Year Final Research Report
Research of Ricci soliton in terms of Submanifold theory
| Project/Area Number |
24540080
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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 | Ibaraki University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Keywords | ガウス写像 / 実超曲面 / 四元数ケーラー構造 / ホップ超曲面 / Austere 部分多様体 |
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| Outline of Final Research Achievements |
In differential geometry, Gauss map is very important to study geometric structure of surfaces and submanifolds. We define a Gauss map from real hypersurface in complex projective space to oriented complex 2-plane Grassmannian. We showed that if a real hypersurface is not Hopf, then the Gauss map is an immersion. If a real hypersurface is Hopf, then the image under the Gauss map is a Kahler submanifold and the Hopf hypersurface is the total space of a circle bundle over Kahler manifold.
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| Free Research Field |
微分幾何学
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