On CR-Lightlike Product of an Indefinite Kaehler Manifold

The geometry of CR-submanifolds of Kaehler manifolds was initiated by Bejancu 1 and has been developed by 2–5 and others. They studied the geometry of CR-submanifolds with positive definite metric. Thus, this geometry may not be applicable to the other branches of mathematics and physics, where the metric is not necessarily definite. Moreover, because of growing importance of lightlike submanifolds and hypersurfaces in mathematical physics, especially in relativity, make the geometry of lightlike submanifolds and hypersurfaces a topic of chief discussion in the present scenario. In the establishment of the general theory of lightlike submanifolds and hypersurfaces, Kupeli 6 and Duggal and Bejancu 7 played a very crucial role. The objective of this paper is to study CR-lightlike submanifolds of an indefinite Kaehler manifold. This motivated us to study CR-lightlike submanifolds extensively.