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 Generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a non-symmetric non-metric connection of type (l, m) Commun. Korean Math. Soc.Published online June 2, 2020 Chul Woo Lee and Jae Won Lee Kyungpook National University, Gyeongsang National University Abstract : Jin \cite{Jin4} defined a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. He said that this connection is an {\it $(\ell,\,m)$-type connection}. Jin also studied lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an $(\ell, m)$-type connection in \cite{Jin4}. We study further the geometry of this subject. In this paper, we study generic lightlike submanifolds of an indefinite trans-Sasakian manifold endowed with an $(\ell, m)$-type connection. Keywords : $(\ell, m)$-type connection, generic lightlike submanifold, indefinite trans-Sasakian structure MSC numbers : 53C25, 53C40, 53C50 Full-Text :