Non-compact Einstein manifolds with symmetry

2021/07/09 by Böhm, Christoph, Lafuente, Ramiro A. · 5 citations
#14L24 #53C25 #53C30 #57S20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.04210

Abstract

For Einstein manifolds with negative scalar curvature admitting an isometric action of a Lie group G with compact, smooth orbit space, we show the following rigidity result: The nilradical N of G acts polarly, and 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.

Cited by

• Counting Homogeneous Einstein Metrics
• Invariant Einstein metrics on basic classical Lie supergroups
• Einstein metrics and Killing spinors on pseudo-Riemannian solvmanifolds
• Finite extinction time of a family of homogeneous Ricci flows
• Almost abelian pseudo-Kähler Lie algebras

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• Einstein solvmanifolds have maximal symmetry
• New homogeneous Einstein metrics of negative Ricci curvature
• New examples of non-symmetric Einstein solvmanifolds of negative Ricci curvature