On normal CR-submanifolds of S-manifolds

0. Introduction. Many authors have studied the geometry of sub-manifolds of Kaehlerian and Sasakian manifolds. On the other hand, DavidE. Blair has initiated the study of S-manifolds, which reduce, in particularcases, to Sasakian manifolds ([1, 2]).I. Mihai ([8]) and L. Ornea ([9]) have investigated CR-submanifolds ofS-manifolds. The purpose of the present paper is to study a special kind ofsuch submanifolds, namely the normal CR-submanifolds.In Sections 1 and 2, we review basic formulas and definitions for sub-manifolds in Riemannian manifolds and in S-manifolds, respectively, whichwe shall use later. In Section 3, we introduce normal CR-submanifolds ofS-manifolds and we study some properties of their geometry. Finally, in Sec-tion 4, we consider those submanifolds in the case of the ambient S-manifoldbeing an S-space form.1. Preliminaries. Let N be a Riemannian manifold of dimension nand M an m-dimensional submanifold of N. Let g be the metric tensor fieldon N as well as the induced metric on M. We denote by ∇ the covariantdifferentiation in N and by ∇ the covariant differentiation in M determinedby the induced metric. Let T(N) (resp. T(M)) be the Lie algebra of vectorfields in N (resp. in M) and T(M)