Statistical structures and Killing vector fields on tangent bundles with respect to two different metrics

Yıl 2023, Cilt: 72 Sayı: 3, 815 - 825, 30.09.2023

Murat Altunbaş

https://doi.org/10.31801/cfsuasmas.1160135

Öz

Let $(M,g)$ be a Riemannian manifold and $TM$ be its tangent bundle. The purpose of this paper is to study statistical structures on $TM$ with respect to the metrics $G_{1}=^{c}g+^{v}(fg)$ and $G_{2}=^{s}g_{f}+^{h}g,\ $ where $f$ is a smooth function on $M,$ $^{c}g$ is the complete lift of $g$, $^{v}(fg)$ is the vertical lift of $fg$, $^{s}g_{f}$ is a metric obtained by rescaling the Sasaki metric by a smooth function $f$ and $^{h}g$ is the horizontal lift of $g.$ Moreover, we give some results about Killing vector fields on $TM$ with respect to these metrics.

Anahtar Kelimeler

Statistical manifold, Riemannian metric, tangent bundle

Kaynakça

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