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International Journal of Mathematics and Mathematical Sciences
Volume 6, Issue 2, Pages 313-326
http://dx.doi.org/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 Hindawi Publishing Corporation. 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).