Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds

3 February 2020
14:15
Christoph Bohm
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.

  • Geometry and Analysis Seminar