Bulletin of the
Korean Mathematical Society BKMS

We introduce $GCR$-lightlike submanifold of a semi-Riemann\-ian product manifold and give an example. We study geodesic $GCR$-lightlike submanifolds of a semi-Riemannian product manifold and obtain some necessary and sufficient conditions for a $GCR$-lightlike submanifold to be a $GCR$-lightlike product. Finally, we discuss minimal $GCR$-lightlike submanifolds of a semi-Riemannian product manifold.

Keywords: $CR$-lightlike submanifolds, $SCR$-lightlike submanifolds, $GCR$-lightlike submanifolds, semi-Riemannian product manifold, minimal lightlike submanifolds

MSC numbers: 53C15, 53C40, 53C50