Let (M,g,∇(α)) be a statistical manifold and g : TM → T ∗ M be a musical isomorphism from the tangent bundle onto the cotangent bundle. Using the α-vertical and α-horizontal lifts on the tangent bundle of the statistical manifold M, we construct the g-α-vertical and g-α-horizontal lifts on the cotangent bundle with the aid of the musical isomorphism g. We prove that the Lie bracket of the α-horizontal lifts of vector fields to tangent and cotangent bundles is g-related if and only if the α-curvature tensor is an even function of α. Also, we get statistical structures via the musical isomorphism in the cotangent bundle. Finally, we give the notion of the Schouten–Van Kampen (α)-connection associated with the statistical connection on the cotangent bundles. Furthermore, we provide some non-trivial examples as applications to this study.
