Submanifolds with flat normal bundle in spaces of constant curvature

In the present paper parallel submanifolds and focal points of a given submanifold with flat normal bundle are discussed provided that the ambient space has constant sectional curvature. We present shape operators of parallel submanifolds with respect to arbitrary normal vectors. Furthermore, we prove that the focal points of a submanifold with flat normal bundle form totally geodesic hypersurfaces in the normal submanifolds.Supported by Hungarian Nat. Found. for Sci. Research Grant No. 1615 (1991).Dedicated to Professor J. Strommer on the occasion of his 75th birthday