Ricci tensor for $GCR$-lightlike submanifolds of indefinite Kaehler manifolds

Abstract

We obtain the expression of Ricci tensor for a $GCR$-lightlike<br />submanifold of indefinite complex space form and discuss its<br />properties on a totally geodesic $GCR$-lightlike submanifold of an<br />indefinite complex space form. Moreover, we have proved that every<br />proper totally umbilical $GCR$-lightlike submanifold of an<br />indefinite Kaehler manifold is a totally geodesic $GCR$-lightlike<br />submanifold.