Uniqueness of Kähler-Ricci solitons on compact kähler manifolds

Gang Tian; Zhu Xiaohua

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

Uniqueness of Kähler-Ricci solitons on compact kähler manifolds

Gang Tian, Zhu Xiaohua

Mathematics

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

9 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.

Original language	English (US)
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

General Mathematics

Access to Document

10.1016/S0764-4442(00)88625-5

Cite this

@article{857ddffb3acd47d9bfe3e8dd731af523,

title = "Uniqueness of K{\"a}hler-Ricci solitons on compact k{\"a}hler manifolds",

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",

month = dec,

day = "1",

doi = "10.1016/S0764-4442(00)88625-5",

language = "English (US)",

volume = "329",

pages = "991--995",

journal = "Comptes Rendus de l'Academie des Sciences - Series I: Mathematics",

issn = "0764-4442",

publisher = "Academie des sciences",

number = "11",

}

TY - JOUR

T1 - Uniqueness of Kähler-Ricci solitons on compact kähler manifolds

AU - Tian, Gang

AU - Xiaohua, Zhu

PY - 1999/12/1

Y1 - 1999/12/1

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.

UR - https://www.scopus.com/pages/publications/0033426768

UR - https://www.scopus.com/inward/citedby.url?scp=0033426768&partnerID=8YFLogxK

U2 - 10.1016/S0764-4442(00)88625-5

DO - 10.1016/S0764-4442(00)88625-5

M3 - Article

AN - SCOPUS:0033426768

SN - 0764-4442

VL - 329

SP - 991

EP - 995

JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

IS - 11

ER -

Uniqueness of Kähler-Ricci solitons on compact kähler manifolds

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this