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

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... lightlike hypersurface of an (ε)-para Sasakian manifolds with a semi-symmetric non-metric connection. 2010 Mathematics Subject Classification. Primary 53C25; Secondary 53C15, 53C40, 53C50 Keywords. (ε)-para Sasakian manifold, lightlike hypersurface, invariant lightlike hypersurface, screen semi-invariant lightlike hypersurface, semi-symmetric non-metric connection.