Statistical structures on tangent bundles and tangent Lie groups

Objective & Hypothesis: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 $g$.

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Key Findings & Data:The purpose of the paper is two folds.

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Conclusion & Impact:Series, 2018] and study statistical structures in this setting.

🔬Design:Research Article

📍Scope:2018 Verileri

⚙️Variables:Metric · statistical structure · tangent bundle

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

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Cite This Article

Peyghan, E., Seifipour, D., Gezer, A. (2021). Statistical structures on tangent bundles and tangent Lie groups. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 4. https://doi.org/10.15672/hujms.645070

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