Duke Mathematical Journal

Ricci flow on Kähler-Einstein manifolds

X. X. Chen and G. Tian

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Abstract

This is the continuation of our earlier article [10]. For any Kähler-Einstein surfaces with positive scalar curvature, if the initial metric has positive bisectional curvature, then we have proved (see [10]) that the Kähler-Ricci flow converges exponentially to a unique Kähler-Einstein metric in the end. This partially answers a long-standing problem in Ricci flow: On a compact Kähler-Einstein manifold, does the Kähler-Ricci flow converge to a Kähler-Einstein metric if the initial metric has positive bisectional curvature? In this article we give a complete affirmative answer to this problem

Article information

Source
Duke Math. J. Volume 131, Number 1 (2006), 17-73.

Dates
First available in Project Euclid: 15 December 2005

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1134666121

Digital Object Identifier
doi:10.1215/S0012-7094-05-13112-X

Mathematical Reviews number (MathSciNet)
MR2219236

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx] 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]

Citation

Chen, X. X.; Tian, G. Ricci flow on Kähler-Einstein manifolds. Duke Math. J. 131 (2006), no. 1, 17--73. doi:10.1215/S0012-7094-05-13112-X. http://projecteuclid.org/euclid.dmj/1134666121.


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