unicité des solitons de Kähler-Ricci solitons sur des variétés kählériennes compactes

Gang Tian; Zhu Xiaohua

doi:10.1016/S0764-4442(00)88625-5

unicité des solitons de Kähler-Ricci solitons sur des variétés kählériennes compactes

Translated title of the contribution: Uniqueness of Kähler-Ricci solitons on compact kähler manifolds

Gang Tian, Zhu Xiaohua

Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We introduce a new holomorphic invariant on any compact Kähler manifolds with positive first Chern 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 Kähler-Ricci solitons. By solving a complex Monge-Ampère equation, we prove the uniqueness of Kähler-Ricci solitons.

Translated title of the contribution	Uniqueness of Kähler-Ricci solitons on compact kähler manifolds
Original language	French
Pages (from-to)	991-995
Number of pages	5
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	329
Issue number	11
DOIs	https://doi.org/10.1016/S0764-4442(00)88625-5
State	Published - Dec 1 1999

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1016/S0764-4442(00)88625-5

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title = "unicit{\'e} des solitons de K{\"a}hler-Ricci solitons sur des vari{\'e}t{\'e}s k{\"a}hl{\'e}riennes compactes",

abstract = "We introduce a new holomorphic invariant on any compact K{\"a}hler manifolds with positive first Chern 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 K{\"a}hler-Ricci solitons. By solving a complex Monge-Amp{\`e}re equation, we prove the uniqueness of K{\"a}hler-Ricci solitons.",

author = "Gang Tian and Zhu Xiaohua",

year = "1999",

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AU - Tian, Gang

AU - Xiaohua, Zhu

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N2 - We introduce a new holomorphic invariant on any compact Kähler manifolds with positive first Chern 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 Kähler-Ricci solitons. By solving a complex Monge-Ampère equation, we prove the uniqueness of Kähler-Ricci solitons.

AB - We introduce a new holomorphic invariant on any compact Kähler manifolds with positive first Chern 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 Kähler-Ricci solitons. By solving a complex Monge-Ampère equation, we prove the uniqueness of Kähler-Ricci solitons.

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JF - Comptes Rendus Mathematique

IS - 11

ER -

unicité des solitons de Kähler-Ricci solitons sur des variétés kählériennes compactes

Abstract

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