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
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.
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).