Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric

Authors : Vladimir BALAN, E PEYGHAN, Esa SHARAHİ

Pages : 120-135

Doi:10.15672/HJMS.2019.667

View : 25 | Download : 7

Publication Date : 2020-02-06

Article Type : Research Paper

Abstract :The first part of the paper is devoted to the classification of the statistical structures which 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 introduce a family of almost complex structures on the tangent bundle equipped with the Sasaki metric, and find equivalent conditions for which this family induces a Kähler structure. Finally, we derive equivalent conditions for existence of holomorphic structures on the tangent bundle equipped with the Sasaki metric in the presence of a statistical structure. Several illustrative examples are provided, as well.
Keywords : Holomorphic statistical manifold, statistical structure, Kähler structure, Sasaki metric