Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds
Differential Geometry
2022-06-29 v1
Abstract
We show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using 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.
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Cite
@article{arxiv.1811.12594,
title = {Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds},
author = {Christoph Böhm and Ramiro A. Lafuente},
journal= {arXiv preprint arXiv:1811.12594},
year = {2022}
}
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23 pages