| Project/Area Number |
17K05235
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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 | Numazu National College of Technology |
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Principal Investigator |
Sawai Hiroshi 沼津工業高等専門学校, 教養科, 准教授 (70550482)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 可解多様体 / べき零多様体 / 局所共形ケーラー構造 / Vaisman 構造 / 複素構造 / ケーラー構造 / 局所共形シンプレクティック構造 / 複素多様体 |
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| Outline of Final Research Achievements |
On locally conformal geometry, if Lee form is parallel, then it is called a Vaisman structure. It is known that Inoue surface, which is a solvmanifold, has a non-Vaisman locally conformal Kahler structure. We generalised Inoue surface and constructed solvmanifolds without locally conformal Kahler structures. Next, we asked for a sufficient condition for a Vaisman structure on locally conformal Kahler solvmanifolds. Moreover, we had the structure theorem for a Vaisman solvmanifold and constructed the new example of a Vaisman solvmanifold.
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| Academic Significance and Societal Importance of the Research Achievements |
可解多様体である井上曲面や O-T 多様体は非 Vaisman な局所共形ケーラー構造をもち, これらは, 計量や複素構造を変形しても, Vaisman 構造をもたないことは, 個別に知られていた. 本研究によって, これらは統一的に, Vaisman 構造をもたないことは示される. さらに, Vaisman 可解多様体は Kodaira-Thurston 多様体とエルミート多様体のある種の意味で同値であることが知られていたが, これを推し進め, Vaisman 可解多様体の構造に言及した.
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