Abstract
We study codimension 2 homogeneous submanifolds of Euclidean space for which the index of minimum relative nullity is small. We prove that if minx∈Mνf(x)≤n-5, where ν(x) denotes the nullity of the second fundamental form of the immersion f at the point x, then the manifold Mn is either isometric to a sphere or to a product of two spheres S2×Sn−2 or covered by the Riemannian product Sn−1 ×R. As a consequence, we obtain a classification of compact codimension 2 homogeneous submanifolds of dimension at least 5.
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De Castro, H.P., Noronha, M.H. Homogeneous Submanifolds of Codimension Two. Geometriae Dedicata 78, 89–110 (1999). https://doi.org/10.1023/A:1005263631283
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DOI: https://doi.org/10.1023/A:1005263631283