On normal CR-submanifolds of S-manifolds

Many authors have studied the geometry of submanifolds of Kaehlerian and Sasakian manifolds. On the other hand, David E. Blair has initiated the study of S-manifolds, which reduce, in particular cases, to Sasakian manifolds ([1, 2]). I. Mihai ([8]) and L. Ornea ([9]) have investigated CR-submanifolds of S-manifolds. The purpose of the present paper is to study a special kind of such submanifolds, namely the normal CR-submanifolds. In Sections 1 and 2, we review basic formulas and definitions for submanifolds in Riemannian manifolds and in S-manifolds, respectively, which we shall use later. In Section 3, we introduce normal CR-submanifolds of S-manifolds and we study some properties of their geometry. Finally, in Section 4, we consider those submanifolds in the case of the ambient S-manifold being an S-space form.