Submanifolds of para-sasakian manifolds

This study which is designed as a philosophy doctoral thesis covers three chapters. In the rst chapter, we give some basic concepts such as semi-Riemannian manifolds, the lightlike hypersurfaces and the lightlike submanifolds of semi-Riemannian manifolds, almost paracontact manifolds for the rest of the thesis that readers can easily understand. The other chapters are the original parts of this thesis. In the second chapter, we study non-degenerate submanifolds of para-Sasakian manifolds. Firstly we obtain su cient and necessary conditions for an invariant submanifold of a para-Sasakian manifold to be semi-parallel and 2-semi-parallel, respectively. After we introduce semi-invariant submanifolds of a para-Sasakian manifold and give some examples. Moreover integrability conditions for some distributions on a semi-invariant submanifold of a para-Sasakian manifold are investigated. Third chapter is devoted to the lightlike geometry of para-Sasakian manifolds. In this chapter, we rstly study lightlike hypersurfaces of para-Sasakian manifolds. After we introduce invariant and screen semi-invariant lightlike hypersurfaces of para-Sasakian manifolds and give some examples. Some results for screen semi-invariant lightlike hypersurfaces of a para-Sasakian space form are obtained. In this chapter we nally investigate invariant, paracontact CR-lightlike and radical transversal lightlike submanifolds of para-Sasakian manifolds.