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 $GCR$-lightlike submanifolds of a semi-Riemannian product manifold Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 883-899 https://doi.org/10.4134/BKMS.2014.51.3.883Published 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 Downloads: Full-text PDF