Kähler--Ricci solitons on toric manifolds with positive first Chern class
type: Item
instance of: scholarly article
title: Kähler--Ricci solitons on toric manifolds with positive first Chern class
zbMATH Open document ID: 1086.53067
author: Xu-Jia Wang
author: Xiaohua Zhu
published in: Advances in Mathematics
publication date: 2004-10-01T00:00:00Z
review text: The authors give a complete solution to the problem of existence of Kähler-Einstein matrices or Kähler-Ricci solitons, unique up to holomorphic automorphisms, on any toric Kähler manifold with positive first Chern class. Moreover, there exists a Kähler-Ricci soliton on a compact complex surface with positive first Chern class, and a soliton is a Kähler metric if and only if the Futaki invariant vanishes. For a toric Fano manifold there exists a Kähler-Einstein metric if and only if the Futaki invariant vanishes and this implies that the holomorphic automorphism group of the manifold is reductive.
reviewed by: Jan Kurek
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 58E11
zbMATH DE Number: 2105307
zbMATH Keywords: Kähler-Ricci soliton
zbMATH Keywords: toric Fano manifold
MaRDI profile type: Publication
full work available at URL: j.aim.2003.09.009
OpenAlex ID: W2046153042
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DOI: 10.1016/J.AIM.2003.09.009
description: scientific article; zbMATH DE number 2105307