Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds
Christoph Böhm, R Lafuente
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.
Topics & Concepts
EinsteinMathematicsHomogeneousEuclidean geometryCurvaturePure mathematicsEinstein's constantConstruct (python library)Lyapunov functionMathematical analysisGeometryMathematical physicsComputer sciencePhysicsCombinatoricsProgramming languageQuantum mechanicsNonlinear systemGeometry and complex manifoldsGeometric Analysis and Curvature FlowsBlack Holes and Theoretical Physics