GEOMETRY OF HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD WITH A QUARTER-SYMMETRIC METRIC CONNECTION

Abstract

Abstract. In this paper, we study the geometry of half lightlikesubmanifolds of an inde nite Kaehler manifold equipped with aquarter-symmetric metric connection. The main result is to proveseveral classi cation theorems for such half lightlike submanifolds. 1. IntroductionA linear connection r on a semi-Riemannian manifold (M; g) is calleda quarter-symmetric connection if its torsion tensor T satis esT(X;Y) = ˇ(Y)˚X ˇ(X)˚Yfor any vector elds X and Y on M, where ˚is a (1;1)-type tensor eld, and ˇis a 1-form associated with a non-vanishing smooth vector eld , which is called the torsion vector eld of M, by ˇ(X) = eg(X;).Moreover, if r is satis ed rg = 0, then it is called a quarter-symmetricmetric connection.The notion of the quarter-symmetric metric connection was intro-duced by K. Yano and T. Imai [17], and since then it have been studiedby S.C. Rastogi [15, 16], D. Kamilya and U.C. De [11], R.S. Mishra andS.N. Pandey [12], S. Golab [6] and many others.The study of lightlike submanifolds was initiated by Duggal and Be-jancu [2] and later studied by many authors (see up-to date results in[4, 5]). Its theory is an important topic of research in di erential ge-ometry due to its application in mathematical physics, especially in thegeneral relativity. The class of codimension 2 lightlike submanifoldsof semi-Riemannian manifolds is composed of two classes by virtue of