# Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds

@article{Bohm2022HomogeneousEM, title={Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds}, author={Christoph Bohm and Ramiro A. Lafuente}, journal={Geometry \& Topology}, year={2022} }

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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