NON-COMPACT EINSTEIN MANIFOLDS WITH SYMMETRY

被引：16
作者：
Boehm, Christoph [1 ]
Lafuente, Ramiro A. [2 ]
机构：
[1] Univ Munster, Einsteinstr 62, D-48149 Munster, Germany
[2] Univ Queensland, Sch Math & Phys, St Lucia, Qld 4072, Australia
来源：
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 36卷 / 03期
基金：
澳大利亚研究理事会;
关键词：
RICCI CURVATURE; PRINCIPAL EIGENVALUE; METRICS; SOLVMANIFOLDS; SOLITONS; CONJECTURE; THEOREM; SPACES; CONE;
D O I：
10.1090/jams/1022
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For Einstein manifolds with negative scalar curvature admitting an isometric action of a Lie group G with compact, smooth orbit space, we show that the nilradical N of G acts polarly and that the 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. © 2023, American Mathematical Society. All rights reserved.
引用
收藏
页码：591 / 651
页数：61
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