Communications of the
Korean Mathematical Society CKMS

In this paper, we study the geometry lightlike hypersurfaces $(M, g, S(TM))$ of a semi-Riemannian manifold $(\widetilde{M}, \widetilde{g})$ of quasi-constant curvature subject to the conditions: (1) The curvature vector field of $\widetilde{M}$ is tangent to $M$, and (2) the screen distribution $S(TM)$ is either totally geodesic in $M$ or totally umbilical in $\widetilde{M}$.

Keywords: totally geodesic, totally umbilical, lightlike hypersurface, semi-Riemannian manifold of quasi-constant curvature

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