Communications of the
Korean Mathematical Society CKMS

We define a new connection on a semi-Riemannian manifold. Its notion contains two well known notions; (1) semi-symmetric connection and (2) quarter-symmetric connection. In this paper, we study the geometry of lightlike hypersurfaces of an indefinite generalized Sasakian space form with a symmetric metric connection of type $(\ell,\,m)$.

Keywords: symmetric connection of type $(\ell,\,m)$, metric connection, lightlike hypersurface

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