In this paper we study invariant lightlike submanifolds of Lorentzian para-sasakian manifolds. We investigate geodesic CR-lightlike submanifolds of Lorentzian para-sasakian manifolds. We study screen CR-lightlike submanifolds of Lorentzian para-sasakian manifolds. Some necessary and sufficient conditions for mixed geodesic, totally geodesic, D ¯ -geodesic and D ˊ -geodesic contact CR-lightlike submanifolds and SCR-lightlike submanifolds are obtained.

In this paper, an induced connection on a Hyper surface ofa semi-almost Hermitian manifold equipped with a quarter-symmetric non-metric connection is studied and proved that induced connection is also a quarter-symmetricnon-metric connection.Further, we have obtained We ingarten equation, equation of Gauss curvature and the Codazzi Main ardiequation of hyper surface of a semi-almost Hermitian manifold equipped with a quarter-symmetric non-metric connection. AMS Mathematics Subject Classification (2010): 53C07,53C26,53C42,53C55