The quaternionic holomorphic differential geometry of totally complex submanifolds
| Project/Area Number |
25400065
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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 | Ochanomizu University |
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Principal Investigator |
TSUKADA KAZUMI お茶の水女子大学, 基幹研究院, 教授 (30163760)
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| Co-Investigator(Kenkyū-buntansha) |
江尻 典雄 名城大学, 理工学部, 教授 (80145656)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 四元数多様体 / 全複素部分多様体 / 四元数射影空間 / 複素グラスマン多様体 / 横断的複素部分多様体 / ツイスター空間 / 四元数複素微分幾何学 / 結合的グラスマン多様体 / 実グラスマン多様体 |
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| Outline of Final Research Achievements |
We studied complex submanifolds of quaternionic manifolds and quaternionic Kaehler manifolds. We developed the theory of transversally complex submanifolds in a quaternion projective space. We found the (2,0)+(0,2)-part of the second fundamental form and the function S whose values are complex structures of a quaternionic vector space as the invariants of the quaternionic differential geometry. We studied the theory of the construction and the classification of totally complex submanifolds in a complex Grassmann manifold of 2-planes. We showed that the projective cotangent bundle of a complex projective space is a twistor space of the complex Grassmann manifold. Applying this fact, we construct maximal totally complex submanifolds of the complex Grassmann manifold from complex submanifolds of a complex projective space.
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Report
(5 results)
Research Products
(14 results)
