Communications of the
Korean Mathematical Society CKMS

We study lightlike hypersurfaces of a semi-Riemannian space form $\widetilde{M}(c)$ admitting a semi-symmetric non-metric connection. First, we construct a type of lightlike hypersurfaces according to the form of the structure vector field of $\widetilde{M}(c)$, which is called a ascreen lightlike hypersurface. Next, we prove a characterization theorem for such an ascreen lightlike hypersurface endow with a totally geodesic screen distribution.

Keywords: totally geodesic, ascreen lightlike hypersurface, semi-symmetric non-metric connection

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