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Generalized Cauchy--Riemann lightlike submanifolds of Kaehler manifolds
Authors:K L Duggal  B Sahin
Institution:(1) Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario, Canada N9B 3P4;(2) Department of Mathematics, Inonu University, 44280, Malatya, Turkey
Abstract:Summary 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.
Keywords:CR-submanifold  degenerate metric  Kaehler manifold
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