Compact homogeneous Einstein manifolds in codimension two

Abstract

In this paper we study compact Riemannian homogeneous submanifolds of Euclidean spaces in codimension 2 for which the metric is Einstein. We prove that they are spheres or product of spheres. We apply this result to study compact cohomogeneity one hypersurfaces whose principal orbits are Einstein manifolds. In the case that they are irreducible manifolds, we conclude that the cohomogeneity one manifold is immersed as a hypersurface of revolution.