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

Authors : Murat ALTUNBAŞ

Pages : 815-825

Doi:10.31801/cfsuasmas.1160135

View : 26 | Download : 55

Publication Date : 2023-09-30

Article Type : Research Paper

Abstract :Let $insert ignore into journalissuearticles values(M,g);$ 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 $G_{1}=^{c}g+^{v}insert ignore into journalissuearticles values(fg);$ and $G_{2}=^{s}g_{f}+^{h}g,\\ $ where $f$ is a smooth function on $M,$ $^{c}g$ is the complete lift of $g$, $^{v}insert ignore into journalissuearticles values(fg);$ 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.
Keywords : Statistical manifold, Riemannian metric, tangent bundle