TRANSVERSAL HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE SASAKIAN MANIFOLD

Abstract

Abstract. In this paper, we study the geometry of half lightlike sub-manifolds of an indefinite Sasakian manifold. There are several differenttypes of half lightlike submanifolds of an indefinite Sasakian manifold ac-cording to the form of its structure vector field. We study two types ofthem here: tangential and ascreen half lightlike submanifolds. 1. IntroductionThe class of codimension 2 lightlike submanifolds of semi-Riemannian man-ifolds is compose of two classes by virtue of the rank of its radical distribution,which are called half lightlike submanifold or coisotropic submanifold [5]. Halflightlike submanifold is a particular case of r-lightlike submanifold [4] suchthat r = 1 and its geometry is more general form than that of coisotrophicsubmanifolds or lightlike hypersurfaces. Much of the works on half lightlikesubmanifolds will be immediately generalized in a formal way to arbitrary r-lightlike submanifolds. Recently many authors have studied the geometry oflightlike submanifolds of indefinite Sasakian manifolds [7, 8, 9, 12].In this paper, we study two types of half lightlike submanifolds of an indefi-nite Sasakian manifold, named by tangential and ascreen half lightlike subman-ifolds. In Section 3, we prove three characterization theorems for tangentialhalf lightlike submanifolds: (1) There exists no screen conformal tangentialhalf lightlike submanifold of an indefinite Sasakian manifold. (2) There ex-ists no tangential half lightlike submanifold of an indefinite Sasakian manifoldsuch that its screen distribution is totally umbilical. (3) There exists no to-tally umbilical tangential half lightlike submanifold of an indefinite Sasakianmanifold.In Section 4, we prove three characterization theorems for ascreen half light-like submanifolds: (1) There exists no screen conformal ascreen half lightlikesubmanifold of an indefinite Sasakian manifold. (2) There exists no ascreen half