Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds

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.