Communications of the
Korean Mathematical Society CKMS

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: Primary 53C25, 53C40, 53C50

Supported by: Chul Woo Lee was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018 R1D1A1B07040576)