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arXiv · 2107.04210

Non-compact Einstein manifolds with symmetry

Christoph Böhm·Ramiro A. Lafuente
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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.

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Christoph Böhm, Ramiro A. Lafuente. 2021-07-09. Non-compact Einstein manifolds with symmetry. https://arxiv.org/abs/2107.04210

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