| Project/Area Number |
09640094
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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 fisheries |
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Principal Investigator |
TSUBOI Kenji Tokyo University of Fisheries, Department of Fisheris, Associate Professor, 水産学部, 助教授 (50180047)
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| Co-Investigator(Kenkyū-buntansha) |
KAMIMURA Yutaka Tokyo University of Fisheries, Department of Fisheris, Associate Professor, 水産学部, 助教授 (50134854)
FUTAKI Akito Tokyo Institute of Technology, Department of mathematics, Professor, 理学部, 教授 (90143247)
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| Project Period (FY) |
1997 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2000: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1999: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1997: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | Complex manifold / Futaki invariant / Einstein metric / Dirac operator / the lifted Futaki invariants / Bando-Calabi-Futaki invariant / Constant scalar curvature Kahler metric / integral invariants / Band-Calabi-Futaki不変量 / 概複素多様体 / 概複素自己同型写像 / 複素自己同型写像 / 不動点公式 / 自己同型群 / 正則ベクトル場 / アインシュタイン=ケーラー計量 / 障害 / リー群準同型写像 / 閉複素多様体 / 第1チャーン形式 |
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| Research Abstract |
Let M be a closed complex manifold. Then the Futaki invariant is an obstruction to the existence of the Einstein-Kahler metric on M.In K.Tsuboi, The lifted Futaki invariants and the spinc-Dirac operators, Osaka J.Math., vol. 32 (1995), 207-225, we obtain a formula to calculate the lifted Futaki invariant, which is a generalization of the Futaki invariant. In [1] (of the next page), we generalize this formula and obtain a fixed point formula for almost complex manifolds. In [2], we show that the holonomy of a certain line bundle is an obstruction to the existence of the Einstein-Kahler metric. The constant scalar Kahler metric is a generalization of the Einstein-Kahler metric. In [3], [4], the relation of the Bando-Calabi-Futaki invariant, which is an obstruction to the existence of the constant scalar curvature Kahler metric and is an integral invariant, to other geometric invariants are studied. In order to obtain the result about the integral invariant, we need to know about the integral equation, which are studied in [5], [6].
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