The Warped Product Lightlike Submanifold Of Semi-Riemannian Product Maniflolds

In this paper, we study a class of lightlike submanifolds of a semi-Riemannian product manifold-warped product lightlike submanifolds. The research of submanifolds of semi-Riemannian manifolds is a hot problem all long, and the non-degenerate submanifolds have been deliberated widely. But one fails to use, in the usual way, the theory of non-degenerate submanifolds to study the geometry of lightlike subman-ifold owing to the degeneration of lightlike submanifolds. Thus there is any work on the field for a long time, until1996, Duggal and Bejancu started to research the degenerate lightlike geometry systematically in [1]. Later stage, more and more mathematicians and physicists concentrated on lightlike submanifold-s, the application of which in physics is remarkable increasingly. For example, lightlike hypersurfaces play a significant role on conformal Killing horizons and dynamical horizons. We concentrate on warped product lightlike submanifolds, get a class of warped product lightlike submanifolds of the first type semi-Riemannian product manifold, and show this type of lightlike submanifolds can reduce to the geometry of a leaf of its screen distribution. Finally, we provide a general construction method of warped product lightlike submanifolds of the second type semi-Riemannian product manifold.