Codimension Two Homogeneous Sub-manifolds of Space Forms

Abstract

In this paper we study codimension two homogeneous submanifolds of Space Forms for which the index of minimum relative nullity is small. Such submanifolds have been studied in the case that they are immersed into the Euclidean space. Under this assumption on the relative nullity, we investigate the rigidity of the immersion, which in turn implies that the submanifold is the orbit of an isometric action in the ambient space. We also study the non-rigid case, that is, we completely classify the codimension two non-rigid immersions of Riemannian homogeneous manifolds into the sphere and into the Hyperbolic space.