GENERALIZED CAUCHY RIEMANN LIGHTLIKE SUBMANIFOLDS OF KAEHLER MANIFOLDS K. L. DUGGAL ∗ (Windsor) AND B. SAHIN (Malatya) Abstract. We introduce a class of submanifolds, namely, Generalized Cauchy Riemann (GCR) lightlike submanifolds of indefinite Kaehler manifolds. We show that this new class is an umbrella of invariant (complex), screen real [8] and CR lightlike [6] submanifolds. We study the existence (or non-existence) of this new class in an indefinite space form. Then, we prove characterization theorems on the existence of totally umbilical, irrotational screen real, complex and CR minimal lightlike submanifolds. We also give one example each of a non totally geodesic proper minimal GCR and CR lightlike submanifolds. 1. Introduction Cauchy Riemann (CR) submanifolds were introduced by Bejancu [3] as a generalization of complex and totally real submanifolds. Later on, Duggal- Bejancu [6] designed a definition for CR - lightlike submanifolds of Kaehler man- ifolds which excludes the complex and real sub cases. Recently, Duggal-Sahin [8] studied a class, called Screen Cauchy Riemann (SCR) - lightlike submanifolds of an indefinite Kaehler manifold which contains complex and screen real sub cases. However, there is no inclusion relation between SCR and CR classes. Moreover, there does not exist any real SCR - lightlike hypersurfaces. Thus, the original problem (for which CR submanifolds were designed) of finding a class of lightlike submanifolds which is an umbrella of all types of submanifolds still remains unsolved. We, therefore, ask the following question: Find a class of lightlike submanifolds including SCR and CR as sub cases? * Research supported by Natural Sciences and Engineering Research Council of Canada Key words and phrases: Degenerate metric, CR - submanifold, Kaehler manifold 2000 Mathematics Subject Classification. 53C15, 53C40, 53C50. 1