International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 2, Pages 313-326
On contact CR-submanifolds of sasakian manifolds
Department of Mathematics, Faculty of Education, Yamagata University, Yamagata, Japan
Received 9 June 1982; Revised 5 January 1983
Copyright © 1983 Koji Matsumoto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Recently, K.Yano and M.Kon  have introduced the notion of a contact
-submanifold of a Sasakian manifold which is closely similar to the one of a -submanifold of a Kaehlerian manifold defined by A. Bejancu .
In this paper, we shall obtain some fundamental properties of contact -submanifolds of a Sasakian manifold. Next, we shall calculate the length of the second
fundamental form of a contact -product of a Sasakian space form (THEOREM 7.4). At last, we shall prove that a totally umbilical contact -submanifold satisfying certain conditions is totally geodesic in the ambient manifold (THEOREM 8.1).