Normal connection and submanifolds with parallel normal fields in a space of constant curvature

A summary account of the cycle of papers of the authors on submanifolds of a space of constant curvature with a parallel field of p-directions, also containing some new results. In the concluding section there is given a survey of papers on submanifolds of a Riemannian manifold using the concept of normal connection.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 12, pp. 3–30, 1981.