Ricci flow on Kähler manifolds

Xiuxiong Chen; Gang Tian

doi:10.1016/S0764-4442(00)01719-5

Ricci flow on Kähler manifolds

Xiuxiong Chen
, Gang Tian

Mathematics

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

5 Scopus citations

Abstract

In this Note, we announce the result that if M is a Kähler-Einstein manifold with positive scalar curvature, if the initial metric has nonnegative bisectional curvature, and the curvature is positive somewhere, then the Kähler-Ricci flow converges to a Kähler-Einstein metric with constant bisectional curvature.

Original language	English (US)
Pages (from-to)	245-248
Number of pages	4
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	332
Issue number	3
DOIs	https://doi.org/10.1016/S0764-4442(00)01719-5
State	Published - Feb 1 2001

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/S0764-4442(00)01719-5

Cite this

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title = "Ricci flow on K{\"a}hler manifolds",

abstract = "In this Note, we announce the result that if M is a K{\"a}hler-Einstein manifold with positive scalar curvature, if the initial metric has nonnegative bisectional curvature, and the curvature is positive somewhere, then the K{\"a}hler-Ricci flow converges to a K{\"a}hler-Einstein metric with constant bisectional curvature.",

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year = "2001",

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AU - Tian, Gang

PY - 2001/2/1

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N2 - In this Note, we announce the result that if M is a Kähler-Einstein manifold with positive scalar curvature, if the initial metric has nonnegative bisectional curvature, and the curvature is positive somewhere, then the Kähler-Ricci flow converges to a Kähler-Einstein metric with constant bisectional curvature.

AB - In this Note, we announce the result that if M is a Kähler-Einstein manifold with positive scalar curvature, if the initial metric has nonnegative bisectional curvature, and the curvature is positive somewhere, then the Kähler-Ricci flow converges to a Kähler-Einstein metric with constant bisectional curvature.

UR - https://www.scopus.com/pages/publications/18044392363

UR - https://www.scopus.com/pages/publications/18044392363#tab=citedBy

U2 - 10.1016/S0764-4442(00)01719-5

DO - 10.1016/S0764-4442(00)01719-5

M3 - Article

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SN - 0764-4442

VL - 332

SP - 245

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

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

IS - 3

ER -

Ricci flow on Kähler manifolds

Abstract

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