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