We introduce the concept of ε -almost paracontact manifolds, and in particular, of ε -para-Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of ε -para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it cannot admit an εpara Sasakian structure. We show that, for an ε -para Sasakian manifold, the conditions of being symmetric, semi-symmetric, or of constant sectional curvature are all identical. It is shown that a symmetric spacelike resp., timelike ε -para Sasakian manifold M n is locally isometric to a pseudohyperbolic space H n ν 1 resp., pseudosphere S n ν 1 . At last, it is proved that for an ε -para Sasakian manifold the conditions of being Ricci-semi-symmetric, Ricci-symmetric, and Einstein are all identical.
We introduce k-Ricci curvature and k-scalar curvature on lightlike hypersurfaces of a Lorentzian manifold. We establish some inequalities between the extrinsic scalar curvature and the intrinsic scalar curvature. Using these inequalities, we obtain some characterizations on lightlike hypersurfaces. We give some results with regard to curvature invariants and S(n 1 , . . . , n k )-spaces for lightlike hypersurfaces of a Lorentzian manifold.
We study lightlike hypersurfaces of para-Sasakian manifolds tangent to the characteristic vector field. In particular, we define invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, respectively, and give examples. Integrability conditions for the distributions on a screen semi-invariant lightlike hypersurface of para-Sasakian manifolds are investigated. We obtain a para-Sasakian structure on the leaves of an integrable distribution of a screen semi-invariant lightlike hypersurface.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.