Volume 26, issue 2 (2022)

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Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds

Christoph Böhm and Ramiro A Lafuente

Geometry & Topology 26 (2022) 899–936
Abstract

We show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using the fact that they admit periodic, integrally minimal foliations by homogeneous hypersurfaces. For the geometric flow induced by the orbit–Einstein condition, we construct a Lyapunov function based on curvature estimates which come from real GIT.

Keywords
Einstein manifolds, homogeneous spaces, cohomogeneity-one manifold
Mathematical Subject Classification
Primary: 53C25, 53C30
References
Publication
Received: 13 December 2020
Accepted: 6 April 2021
Published: 15 June 2022
Proposed: John Lott
Seconded: Tobias H Colding, Bruce Kleiner
Authors
Christoph Böhm
Mathematisches Institut
University of Münster
Münster
Germany
Ramiro A Lafuente
School of Mathematics and Physics
The University of Queensland, St Lucia campus
Brisbane
Australia