Abstract

In this paper, we prove that there do not exist warped product $GCR$-lightlike submanifolds in the form $M = N_{\bot}\times_{\lambda}N_{\top}$ such that $N_{\bot}$ is an anti-invariant submanifold tangent to $V$ and $N_{\top}$ an invariant submanifold of $\overline{M}$, other than $GCR$-lightlike product in an indefinite Kenmotsu manifold. We also obtain some characterizations for a $GCR$-lightlike submanifold to be locally a $GCR$-lightlike warped product.

Keywords: $GCR$-lightlike submanifold, $GCR$-lightlike product, $GCR$-lightlike warped product submanifold, indefinite Kenmotsu manifold.

MSC: 53C40, 53C42, 53C50, 53C55

Pages:  533$-$546     

Volume  65 ,  Issue  4 ,  2013