Journal of the
Korean Mathematical Society JKMS

We define a new connection on semi-Riemannian manifolds, which is a non-symmetric and non-metric connection. We say that this connection is an $(\ell,\,m)$-type connection. Semi-symmetric non-metric connection and non-metric $\phi$-symmetric connection are two important examples of this connection such that $(\ell,\,m) = (1,\,0)$ and $(\ell,\,m) = (0,\,1)$, respectively. In this paper, we study lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an $(\ell,\,m)$-type connection.

Keywords: $(\ell, m)$-type connection, lightlike hypersurface, indefinite trans-Sasakian manifold

MSC numbers: Primary 53C25, 53C40, 53C50