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Vector Field Energies and Critical Metrics 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, mabuchi@math.wani.osaka-u.ac.jp
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Abstract

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Associated with a Hamiltonian holomorphic vector field on a compact Kähler manifold, a nice functional on a space of Kähler metrics will be constructed as an integration of the bilinear pairing in [FM] contracted with the Hamiltonian holomorphic vector field. As applications, we have functionals whose critical points are extremal Kähler metrics or “Kähler-Einstein metrics” in the sense of [M4], respectively. Finally, the same method as used by [G1] allows us to obtain, from the convexity of , the uniqueness of “Kähler-Einstein metrics” on nonsingular toric Fano varieties possibly with nonvanishing Futaki character.

Keywords

53C5514J4514J5032J25
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 162 , June 2001 , pp. 41 - 63
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

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