International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 331-340
doi:10.1155/S0161171295000421
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 M. Hasan shahid and A. Sharfuddin. 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
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.