CR-submanifolds of Some Lorentzian Manifolds and K-manifolds

Abstract

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(perp)-totally geodesic CR-submanifold, xi-horizontal CR-submanifold where the distribution is integrable (here xi is the structure vector field). Also I have proved some results on D-umbilic CR-submanifold, mixed totally geodesic CR-submanifold, foliate xi-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.