Infinitesimal Affine Transformations and Mutual Curvatures on Statistical Manifolds and Their Tangent Bundles

Abstract

The purpose of this paper is to find some conditions under which the tangent bundle TM has a dualistic structure. Then, we introduce infinitesimal affine transformations on statistical manifolds and investigate these structures on a special statistical distribution and the tangent bundle of a statistical manifold too. Moreover, we also study the mutual curvatures of a statistical manifold M and its tangent bundle TM and we investigate their relations. More precisely, we obtain the mutual curvatures of well-known connections on the tangent bundle TM (the complete, horizontal, and Sasaki connections) and we study the vanishing of them.

Keywords

• infinitesimal affine transformations
• mutual curvature
• statistical manifold
• tangent bundle