Bulletin of the
Korean Mathematical Society BKMS

We define a new connection on semi-Riemannian manifolds, which is called a {\it symmetric connection of type} $(\ell,\,m)$. Semi-symmetric connection and quarter-symmetric connection are two 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 Kaehler manifold endowed 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