2000 Fiscal Year Final Research Report Summary
Einstein metric on complex manifolds and the lifted Futaki invariant
| 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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| Keywords | Complex manifold / Futaki invariant / Einstein metric / Dirac operator / the lifted Futaki invariants / Bando-Calabi-Futaki invariant / Constant scalar curvature Kahler metric / integral invariants |
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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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