Statistical structures on tangent bundles and tangent Lie groups

Authors : Esmaeil PEYGHAN, Davood SEİFİPOUR, Aydın GEZER

Pages : 1140-1154

Doi:10.15672/hujms.645070

View : 19 | Download : 11

Publication Date : 2021-08-06

Article Type : Research Paper

Abstract :Let $TM$ be a tangent bundle over a Riemannian manifold $M$ with a Riemannian metric $g$ and $TG$ be a tangent Lie group over a Lie group with a left-invariant metric $g$. The purpose of the paper is two folds. Firstly, we study statistical structures on the tangent bundle $TM$ equipped with two Riemannian $g$-natural metrics and lift connections. Secondly, we define a left-invariant complete lift connection on the tangent Lie group $TG$ equipped with metric $\tilde{g}$ introduced in [F. Asgari and H. R. Salimi Moghaddam, On the Riemannian geometry of tangent Lie groups, Rend. Circ. Mat. Palermo II. Series, 2018] and study statistical structures in this setting.
Keywords : Metric, statistical structure, tangent bundle, tangent Lie group, lift connection