# Rigged null hypersurfaces in almost paracontact metric manifolds

### Abstract

Given an almost paracontact metric manifold $(\overline {M}, \overline{ \phi},\overline {\eta}, \xi, \overline {g})$, we study lightlike hypersurfaces $M$ of the semi-Riemannian manifold $(\overline {M},\overline{g})$ transversal to the structure vector field $\xi$. The latter is then a rigging for $M$ and defines a null section $E$ of the radical distribution of $M$ and a screen distribution which turns out to be always semi-invariant. We show that leaves of an integrable screen distribution in such hypersurfaces $M$ are almost paracontact metric manifolds too. When the ambient space $(\overline {M}, \overline{ \phi},\overline {\eta}, \xi, \overline {g})$ is para-Sasakian, we show that the screen distribution cannot be conformal and that $E$ is a geodesic vector field in $(M, \nabla),$ where $\nabla$ is the connection induced on $M$ by Levi-Civita connection of $\overline {g}$ and the local null rigging $N=\xi-\frac{1}{2}E$. We also find necessary and sufficient conditions for the leaves of the screen distribution to be para-Sasakian too and finally we investigate integrability conditions for some additional distributions induced on $M$ by the structure $(\overline {M}, \overline{ \phi},\overline {\eta}, \xi, \overline {g})$.

*Gulf Journal of Mathematics*,

*7*(2). Retrieved from https://gjom.org/index.php/gjom/article/view/190