In this paper I have studied about CR(Cauchy-Riemann)-submanifolds of Lorentzian Concircular Structure manifold ((LCS) n -manifold), Lorentzian Para-Sasakian(LP)-cosymplectic manifold, S-manifold and Generalized Kenmotsu (GKM) manifold. I have discussed some results regarding distribution, structure vector field, totally geodesic submanifold, leaf etc.. I have obtained results on totally umbilical contact CR-submanifold where the anti-invariant distribution has some properties. Next, I have studied some results about D-totally geodesic CR-submanifold (D is the distribution), a contact CR-submanifold, D ⊥ -totally geodesic CR-submanifold, ξ-horizontal CR-submanifold where the distribution is integrable (here ξ is the structure vector field). Also I have proved some results on Dumbilic CR-submanifold, mixed totally geodesic CR-submanifold, foliate ξ-horizontal mixed totally geodesic CR-submanifold, leaf of the distribution, totally geodesic leaf, CR-product etc.. I have given an example of a CR-submanifold of an (LCS) n -manifold and at last, I have given an example of a GKM manifold.

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The present paper deals with the study of contact CR-submanifolds of trans-Sasakian manifolds with respect to quarter symmetric non-metric connection. We investigate totally geodesic leaves and integrability of the distributions and also study the totally umbilical contact CR-submanifolds of trans-Sasakian manifolds. At last we give an example to verify a relation.

In this paper we analyse briefly some properties of hemi-slant sub-manifold of (LCS)n-manifold. Here we discuss about some necessary and sufficient conditions for distributions to be integrable and obtain some results in this direction. We also study the geometry of leaves of hemi-slant submanifold of (LCS)n-manifold. At last we give an example of a hemi-slant submanifold of an (LCS)n-manifold.