| Project/Area Number |
15K04839
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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) |
守屋 克洋 筑波大学, 数理物質系, 助教 (50322011)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 四元数多様体 / ツイスター空間 / ツイスターリフト / inclusive immersion / twistor space / twistor lift / 包含的曲面 |
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| Outline of Final Research Achievements |
We study surfaces in a quaternionic manifold. Using the twistor space, which is associted with the quaternionic manifold and has many results, we obtain the results. In particular, we construct a quaternionic invariant for such surfaces, and find the lower bound and its characterization. Moreover the first variation formula is calculated. Some of these result give generalizations and improvements of known theorems.
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| Academic Significance and Societal Importance of the Research Achievements |
上記ような四元数構造は次元が低いときには，共形構造とよばれるものに一致する．したがって，当該の四元数幾何学の研究はこれまで多くの研究がなされている共形幾何学と同様に興味深い結果を得られると期待できるが，本研究で得られた結果はそのような視点で見た場合の部分多様体論における基礎的な結果といえる．
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