$GCR$-lightlike submanifolds of a semi-Riemannian product manifold
Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 883-899
Published online May 31, 2014
Sangeet Kumar, Rakesh Kumar, and Rakesh Kumar Nagaich
Chitkara University, Punjabi University, Punjabi University
Abstract : 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
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