Inequalities on Sasakian Statistical Manifolds in Terms of Casorati Curvatures

Abstract

A statistical structure is considered as a generalization of a pair of a Riemannian metric and its Levi-Civita connection. With a pair of conjugate connections del and del* in the Sasakian statistical structure, we provide the normalized scalar curvature which is bounded above from Casorati curvatures on C-totally real (Legendrian and slant) submanifolds of a Sasakian statistical manifold of constant phi-sectional curvature. In addition, we give examples to show that the total space is a sphere.