A new holomorphic invariant and uniqueness of Kähler-Ricci solitons

Gang Tian, Xiao‐Wei Zhu

Type: Article

Publication Date: 2002-06-30

Citations: 164

DOI: https://doi.org/10.1007/s00014-002-8341-3

Abstract

In this paper, a new holomorphic invariant is defined on a compact Kähler manifold with positive first Chern class and nontrivial holomorphic vector fields.This invariant generalizes the Futaki invariant.We prove that this invariant is an obstruction to the existence of Kähler-Ricci solitons.In particular, using this invariant together with the main result in [TZ1], we solve completely the uniqueness problem of Kähler-Ricci solitons.Two functionals associated to the new holomorphic invariant are also discussed.The main result here was announced in [TZ2].

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+	Kahler-Einstein Metrics and Integral Invariants	1988	Akito Futaki
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+	Kähler-Einstein metrics with positive scalar curvature	1997	Gang Tian
+	None	1999	Henrik Pedersen Christina W. Tønnesen-Friedman Galliano Valent
+	Kähler-Ricci soliton typed equations on compact complex manifolds withC 1(M) > 0	2000	Xiaohua Zhu
+	On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I	1978	Shing‐Tung Yau
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