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International Journal of Mathematics and Mathematical Sciences
Volume 18, Issue 2, Pages 331-340

On Generic submanifolds of a locally conformal Kahler manifold with parallel canonical structures

Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, India

Received 23 March 1993; Revised 1 October 1993

Copyright © 1995 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.


The study of CR-submanifolds of a Kähler manifold was initiated by Bejancu [1]. Since then many papers have appeared on CR-submanifolds of a Kähler manifold. Also, it has been studied that generic submanifolds of Kähler manifolds [2] are generalisations of holomorphic submanifolds, totally real submanifolds and CR-submanifolds of Kähler manifolds. On the other hand, many examples C2 of generic surfaces in which are not CR-submanifolds have been given by Chen [3] and this leads to the present paper where we obtain some necessary conditions for a generic submanifolds in a locally conformal Kähler manifold with four canonical strucrures, denoted by P, F, t and f, to have parallel P, F and t. We also prove that for a generic submanifold of a locally conformal Kähler manifold, F is parallel iff t is parallel.