LAUSR

In the present paper, we study a lightlike hypersurface, when the ambient manifold is an (ε)-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 (ε)-para Sasakian manifolds with a semi-symmetric non-metric connection. Also, we obtain integrability conditions for the distributions D ⊥ 〈δ〉 and D′ ⊥ 〈δ〉 of a screen semi-invariant lightlike hypersurface of an (ε)-para Sasakian manifolds with a semi-symmetric non-metric connection.