Toric extremal Kähler-Ricci solitons are Kähler-Einstein

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2017-12-20 DOI:10.1515/coma-2017-0012

Simone Calamai, David Petrecca

引用次数: 2

Abstract

Abstract In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.

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托里极端Kähler-Ricci孤子是Kächler-Einstein

摘要在这篇短文中，我们证明了紧复曲面Kähler流形上的Calabi极值Kährer-Ricci孤立子是爱因斯坦。这就解决了复曲面流形这类问题，这是作者提出的一个一般问题，他们只在一些曲率假设下求解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.