2004 Fiscal Year Final Research Report Summary
Kahler metrics of constant curvature on complex manifolds and topological invariants
| Project/Area Number |
14540067
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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 | Tokyo University of Marine Science & Technology (TUMST) (2004)
東京水産大学 (2002-2003) |
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Principal Investigator |
TSUBOI Kenji Tokyo University of Marine Science & Technology (TUMST), Faculty of Marine Science, Professor, 海洋科学部, 教授 (50180047)
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| Co-Investigator(Kenkyū-buntansha) |
KAMIMURA Yutaka Tokyo University of Marine Science & Technology (TUMST), Faculty of Marine Science, Professor, 教授 (50134854)
FUTAKI Akito Tokyo Institute of Technology, School of Science, Professor, 理学部, 教授 (90143247)
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| Project Period (FY) |
2002 – 2004
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| Keywords | complex manifolds / Kahler metric of constant curvature / elliptic operator / group action / equivariant determinant / Bando-Calabi-Futaki invariant / fixed point set / rotation angle |
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| Research Abstract |
The Futaki invariant is an obstruction to the existence of Kahler-Einstein metrics. In this research we give an relation between the Futaki invariant and the Witten's holonomy of a fiber bundle with fiber F and base space B where F is a compact complex manifold and B is the circle. This result is published in
K.Tsuboi, On the Einstein-Kahler metric and the holonomy of a line bundle, Proc.Edinburgh Math.Soc., Vol.45(2002), 83-90.
The sphere of zero or one or three dimension have a group structure. In this research using this structure we give a new formula for the fixed point data of finite group action on compact almost complex manifolds. This result is published in
K.Tsuboi, A fixed point formula for compact complex manifolds, J.Math.Kyoto Univ., Vol. 42 (2002), 1-20.
Group action on manifolds represents the symmetry of manifolds. In this research we made a discovery of a new method to use the equivariant determinant of elliptic operators as an obstruction to the existence of finite group actions on compact manifolds. This result is published in
K.Tsuboi, The finite group action and the equivariant determinant of elliptic operators, J.Math.Soc.Japan, vol.57 (2005), 95-113.
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Research Products
(11 results)
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[Book] 数学入門II2004
Author(s)
上村豊, 坪井堅二
Total Pages
280
Publisher
東京化学同人
Description
「研究成果報告書概要(和文)」より
