Communications of the
Korean Mathematical Society CKMS

The main purpose of this paper is to study the lightlike hypersurface $(M,\bar{g})$ of cosymplectic space form $\bar{M}(c)$. In this paper, we computed the Gauss and Codazzi formulae of $(M,\bar{g})$ of cosymplectic manifold $(\bar{M},g)$. We showed that we can't obtain screen semi-invariant lightlike hypersurface (SCI-LH) of $\bar{M}(c)$ with parallel second fundamental form $h$, parallel screen distribution and $c\neq 0$. We showed that if second fundamental form $h$ and local second fundamental form $B$ are parallel, then $(M,\bar{g})$ is totally geodesic. Finally we showed that if $(M,\bar{g})$ is umbilical, then cosymplectic manifold $(\bar{M},g)$ is flat.

Keywords: Lightlike hypersurfaces, cosymplectic space form, second fundamental form, umbilical and totally geodesic lightlike hypersurfaces

MSC numbers: Primary 53D10, 53D25, 53C35