Generalized symmetric metric connection on statistical manifolds

چکیده مقاله

We define the generalized symmetric metric connection of type (α,β) on almost contact statistical manifolds and Sasakian statistical manifolds. The curvature properties of these manifolds admitting such a connection are derived. Additionally, we investigate the symmetry properties of the curvature tensor with respect to this metric connection. New results are presented for Sasakian statistical manifolds equipped with a generalized symmetric metric connection of type (α,β). Finally, explicit examples of Sasakian statistical manifolds are constructed to illustrate the theoretical framework. © 2026 Polish Scientific Publishers.