Non existence of totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds

Abstract

In present paper, after finding the conditions for the integrability of various distributions of a GCR-lightlike submanifold of indefinite Kenmotsu manifolds, we prove that there do not exist totally contact umbilical GCR-lightlike submanifolds of indefinite Kenmotsu manifolds other than totally contact geodesic GCR-lightlike submanifolds and moreover it is a totally geodesic GCR-lightlike submanifold.