Non-compact Einstein manifolds with symmetry
Differential Geometry
2023-01-11 v2
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.
Cite
@article{arxiv.2107.04210,
title = {Non-compact Einstein manifolds with symmetry},
author = {Christoph Böhm and Ramiro A. Lafuente},
journal= {arXiv preprint arXiv:2107.04210},
year = {2023}
}
Comments
54 pages, significant changes in Sections 1 - 8. Final version, to appear in JAMS