CR Lightlike Submanifolds of Indefinite Kaehler Manifolds

Abstract

In this Chapter, we study Cauchy Riemann (CR) lightlike hypersurfaces and submanifolds (in general) of indefinite Hermitian and Kaehler manifolds. We prove that a lightlike real hypersurface M of an indefinite Hermitian manifold is a CR manifold and show that the integrability of all distributions of M is characterized by both second fundamental forms of M and its screen distribution S(TM). Finally, we study the geometry of various foliations on a CR lightlike submanifold and the existence of CR lightlike products of \(\bar M\).