2017 Fiscal Year Final Research Report
Locally homogeneous non-Kaehler manifolds and Transformation groups
| Project/Area Number |
15K04852
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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 | Josai University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
長谷川 敬三 新潟大学, 人文社会・教育科学系, 教授 (00208480)
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| Research Collaborator |
Alekseevsky Dmitri. A. Institute for Information Transmission
Cortés Vicente University of Hamburg, Department of Mathematics and Center for Mathematical Physics
Baues Oliver University of Fribourg, Department of Mathematics
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | LcK structure / Vaisman structure / Kaehler structure / Homogeneous space / Sasaki homogeneous space / Seifert fibering / Unimodular Lie group / Holomorphic Isometry |
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| Outline of Final Research Achievements |
A locally conformal Kaehler structure (lcK structure) on a Hermitian manifold (M,g,J) is the fundamental 2-form Ωsatisfying dΩ =ΩΛθ for some closed 1-form θ. The Lee field A is determined by the formula g(X) = g(A,X). If A is holomorphic Killing, then M is said to be a Vaisman manifold. If a Lie group G admits a left invariant lcK structure, G is said to be an lcK group. We have determined homogeneous Vaisman manifolds. Moreover, we classied unimodular Vaisman lcK groups.
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| Free Research Field |
Geometry and Topology
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