International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 2, Pages 313-326
doi:10.1155/S0161171283000277
On contact CR-submanifolds of Sasakian manifolds
Koji Matsumoto
Department of Mathematics, Faculty of Education, Yamagata University, Yamagata, Japan
Abstract
Recently, K.Yano and M.Kon [5] have introduced the notion of a contact CR-submanifold of a Sasakian manifold which is closely similar to the one of a CR-submanifold of a Kaehlerian manifold defined by A. Bejancu [1]. In this paper, we shall obtain some fundamental properties of contact CR-submanifolds of a Sasakian manifold. Next, we shall calculate the length of the second fundamental form of a contact CR-product of a Sasakian space form (THEOREM 7.4). At last, we shall prove that a totally umbilical contact CR-submanifold satisfying certain conditions is totally geodesic in the ambient manifold (THEOREM 8.1).