| Project/Area Number |
22540071
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Niigata University |
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Principal Investigator |
SEKIGAWA Kouei 新潟大学, 自然科学系, フェロー (60018661)
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| Co-Investigator(Kenkyū-buntansha) |
OGURO Takashi 東京電機大学, 理工学部, 講師 (40297578)
YAMADA Akira 長岡工業高等専門学校, 一般教育科, 准教授 (60311007)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 概エルミート多様体 / ゴールドバーグの予想 / チャーン・ヴェイユ理論 / ガウス・ボンネ・チャーンの定理 / アインシュタイン・ヒルベルト汎関数 / 単位接球面束 / 普遍曲率恒等式 / ボッホナー曲率テンンソル / 概エルミート構造 / Einstein 計量 / Goldberg 予想 / 佐々木多様体 / Chern-Weil 理論 / 特性類 / Gauss-Bonnet の定理 / 臨界概エルミート構造 / Goldberg予想 / Gauss-Bonnet定理 / Einstein計量 / 曲率恒等式 / Chern-Weil理論 / 接触計量多様体 / TV-Bochner曲率テンソル / TV-Bochner平坦概エルミート多様体 / H-接触計量多様体 / 2-stein多様体 / 指数定理 |
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| Research Abstract |
An almost complex manifold quipped with a compatible Riemannian metric is called an almost Hermitian manifold. In our research project, we obtained several interesting results on the topics concerning the integrability of almost Hemitian manifolds and also on various variational problems for the Koda functional which is regarded as an extension of the Einstein-Hilbert functional to almost Hermitian setting. Further,we obtained some results on the unit tangent sphere bundles such that the characteristic vector fields are harmonic vector fields. We also discussed some problems arised in the course of our research activity and could obtain unexpected results.
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