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Uniqueness of Kahler—Ricci solitons on compact Kahler manifolds by Gang Tian; Xiaohua Zhu is a Mathematics article available to read on EtoBox.

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We introduce a new holomorphic invariant on any compact K%hler manifolds with positive first Chem class and nontrivial holomorphic vector fields, which contains the Futaki invariant as a special case. This invariant is shown to be an obstruction to the existence of Kahler-Ricci solitons. By solving a complex Monge-Ampere equation, we prove the uniqueness of Kahler-Ricci solitons. 0 1999 Academic des sciences/Editions scientifiques et medicales Elsevier SAS U&it6 des so&tons de Kihler-Ricci solitons sur des vari6t6s ktihl&ennes compactes RCsumC. On construit un nouvel invariant associe' d une varie'te'kiihle'rienne compacte de premiere classe de Chern positive, etpossedant des champs de vecteurs holomorphes non triviaux. Cet invariant genne'ralise l'invariant de Futaki. On montre que cet invariant est une obstruction a l'existence de solitons de Kiihler-Ricci. Par resolution d'une equation de Mange-Ampere complexe, on montre l'unicite' des solitons de Kahler-Ricci. 0 1999 Academic des sciences/Editions scientifiques et medicales Elsevier SAS Version francake abdg4e Les solitons de Ricci sent relies au comportement limite des solutions d'equations aux derivees pat-belles likes a la g

Who reads Uniqueness of Kahler—Ricci solitons on compact Kahler manifolds?

Author

Gang Tian; Xiaohua Zhu

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0764-4442)

Published

1999

Language

EN

Field

Mathematics (Physical Sciences)