Non-compact Einstein manifolds with symmetry

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2023-02-28 DOI:10.1090/jams/1022

Christoph Böhm, Ramiro A. Lafuente

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引用次数: 4

Abstract

For Einstein manifolds with negative scalar curvature admitting an isometric action of a Lie group G \mathsf {G} with compact, smooth orbit space, we show that the nilradical N \mathsf {N} of G \mathsf {G} acts polarly and that the N \mathsf {N} -orbits can be extended to minimal Einstein submanifolds. As an application, we prove the Alekseevskii conjecture: Any homogeneous Einstein manifold with negative scalar curvature is diffeomorphic to a Euclidean space.

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对称的非紧致爱因斯坦流形

对于允许李群G \mathsf {G}具有紧致光滑轨道空间的等距作用的负标量曲率爱因斯坦流形，我们证明了G \mathsf {G}的零根N \mathsf {N}具有极作用，并且N \mathsf {N}轨道可以扩展到最小爱因斯坦子流形。作为应用，我们证明了Alekseevskii猜想:任何具有负标量曲率的齐次爱因斯坦流形对欧几里德空间都是微分同态的。

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

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.