Kähler-Ricci solitons on toric manifolds with positive first Chern class

Xu Jia Wang; Xiaohua Zhu

doi:10.1016/j.aim.2003.09.009

Kähler-Ricci solitons on toric manifolds with positive first Chern class

Xu Jia Wang^*, Xiaohua Zhu

^*Corresponding author for this work

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

214 Citations (Scopus)

Abstract

In this paper we prove there exists a Kähler - Ricci soliton, unique up to holomorphic automorphisms, on any toric Kähler manifold with positive first Chern class, and the Kähler - Ricci soliton is a Kähler - Einstein metric if and only if the Futaki invariant vanishes.

Original language	English
Pages (from-to)	87-103
Number of pages	17
Journal	Advances in Mathematics
Volume	188
Issue number	1
DOIs	https://doi.org/10.1016/j.aim.2003.09.009
Publication status	Published - 20 Oct 2004

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title = "K{\"a}hler-Ricci solitons on toric manifolds with positive first Chern class",

abstract = "In this paper we prove there exists a K{\"a}hler - Ricci soliton, unique up to holomorphic automorphisms, on any toric K{\"a}hler manifold with positive first Chern class, and the K{\"a}hler - Ricci soliton is a K{\"a}hler - Einstein metric if and only if the Futaki invariant vanishes.",

keywords = "K{\"a}hler-Ricci soliton, Monge-Amp{\`e}re equation, Toric Fano manifold",

author = "Wang, {Xu Jia} and Xiaohua Zhu",

year = "2004",

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day = "20",

doi = "10.1016/j.aim.2003.09.009",

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volume = "188",

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T1 - Kähler-Ricci solitons on toric manifolds with positive first Chern class

AU - Wang, Xu Jia

AU - Zhu, Xiaohua

PY - 2004/10/20

Y1 - 2004/10/20

N2 - In this paper we prove there exists a Kähler - Ricci soliton, unique up to holomorphic automorphisms, on any toric Kähler manifold with positive first Chern class, and the Kähler - Ricci soliton is a Kähler - Einstein metric if and only if the Futaki invariant vanishes.

AB - In this paper we prove there exists a Kähler - Ricci soliton, unique up to holomorphic automorphisms, on any toric Kähler manifold with positive first Chern class, and the Kähler - Ricci soliton is a Kähler - Einstein metric if and only if the Futaki invariant vanishes.

KW - Kähler-Ricci soliton

KW - Monge-Ampère equation

KW - Toric Fano manifold

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U2 - 10.1016/j.aim.2003.09.009

DO - 10.1016/j.aim.2003.09.009

M3 - Article

SN - 0001-8708

VL - 188

SP - 87

EP - 103

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

Kähler-Ricci solitons on toric manifolds with positive first Chern class

Abstract

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