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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| Co-Investigator(Kenkyū-buntansha) |
大塚 富美子 茨城大学, 理学部, 准教授 (90194208)
入江 博 茨城大学, 理学部, 准教授 (30385489)
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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 / ツイスター空間 / 複素グラスマン多様体 / 複素射影空間 / 複素双曲空間 / ルジャンドル部分多様体 / 外的測地線 / 全複素部分多様体 / リッチ・ソリトン / Hopf 超曲面 / Austere 超曲面 / 特殊ラグランジュ部分多様体 |
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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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Report
(6 results)
Research Products
(30 results)
