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Multiplier Hermitian structures on Kähler manifolds

Published online by Cambridge University Press:  22 January 2016

Toshiki Mabuchi
Toshiki Mabuchi*
Affiliation:
Department of Mathematics, Osaka University, Toyonaka, Osaka, 560-0043, Japan, [email protected]
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Abstract

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The main purpose of this paper is to make a systematic study of a special type of conformally Kähler manifolds, called multiplier Hermitian manifolds, which we often encounter in the study of Hamiltonian holomorphic group actions on Kähler manifolds. In particular, we obtain a multiplier Hermitian analogue of Myers’ Theorem on diameter bounds with an application (see [M5]) to the uniquness up to biholomorphisms of the “Kähler-Einstein metrics” in the sense of [M1] on a given Fano manifold with nonvanishing Futaki character.

Keywords

53C5514J4514J5032J25
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 170 , 2003 , pp. 73 - 115
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

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