Some Characterizations of PS-Statistical Manifolds

Abstract

In the present study, firstly we state symmetry properties for curvatures of a statistical manifold and give some relations between the Riemannian curvature b R and the curvatures R; R∗ and RS. After, by defining the notion of para-Sasakian statistical manifold, we give the necessary and sufficient conditions for a structure (D; h; Ψ; w; ζ) to be a para-Sasakian structure when (D; h) is a statistical structure and (Ψ; w; ζ; h) is an almost paracontact Riemannian manifold. Also, we give some results for curvatures R; R∗; RS and Ricci tensor of these curvatures on a para-Sasakian statistical manifold. We construct an example of para-Sasakian statistical manifold of dimension 3. Finally, we examined the Einsteinian of para-Sasakian statistical manifolds according to certain conditions.