Homogeneous Submanifolds of Codimension Two

We study codimension 2 homogeneous submanifolds of Euclidean space for which the index of minimum relative nullity is small. We prove that if min_xMf(x)n-5, where (x) denotes the nullity of the second fundamental form of the immersion f at the point x, then the manifold M ⁿ is either isometric to a sphere or to a product of two spheres S²×S ^n–2 or covered by the Riemannian product S ^n–1 ×R. As a consequence, we obtain a classification of compact codimension 2 homogeneous submanifolds of dimension at least 5.