Lightlike Hypersurfaces of an $(\varepsilon)$-Para Sasakian Manifold with a Semi-Symmetric Non-Metric Connection

Abstract

In the present paper, we study a lightlike hypersurface, when the ambient manifold is an $(\varepsilon)$-para Sasakian manifold endowed with a semi-symmetric non-metric connection. We obtain a condition for such a lightlike
hypersurface to be totally geodesic. We define invariant and screen
semi-invariant lightlike hypersurfaces of $(\varepsilon)$-para Sasakian manifolds with a semi-symmetric non-metric
connection. Also, we obtain integrability conditions for the distributions $D\perp \delta$ and $D^{\prime }\perp \delta  $ of a screen
semi-invariant lightlike hypersurface of an $(\varepsilon)$-para Sasakian manifolds with a semi-symmetric non-metric
connection.