Statistical structures on the tangent bundle of astatistical manifold with Sasaki metric

Abstract

The first part of the paper is devoted to the classification of the statistical structureswhich live on the tangent bundle of a statistical manifold endowed with a Sasaki metric.Further, considering a Kähler structure on the base statistical manifold, we introducea family of almost complex structures on the tangent bundle equipped with the Sasakimetric, and find equivalent conditions for which this family induces a Kähler structure.Finally, we derive equivalent conditions for existence of holomorphic structures on thetangent bundle equipped with the Sasaki metric in the presence of a statistical structure.Several illustrative examples are provided, as well.