Semi-symmetric statistical manifolds

Abstract

This paper studies semi-symmetric statistical manifolds (3S-manifolds for short) to generalise semi-Weyl manifolds. We prove that this class of manifolds is invariant under the conformal change of metrics.  We show that every 3S-structure $(g, \omega, \omega^{\ast}, \nabla)$ on a Riemannian manifold $(M,g)$ induces a statistical structure $(g, \widetilde{\nabla})$  on $M$ and  we find  necessary and  sufficient  conditions for $\nabla$ and $\widetilde{\nabla}$ to have the same sectional  curvature. In addition, the analogue of the statistical Curvature is defined for 3S structures and its properties are investigated. We also give a method to construct 3S structures on a warped product manifold from 3S structures on the fiber and base manifolds.