STATISTICAL STRUCTURES AND KILLING VECTOR FIELDS ON TANGENT BUNDLES WITH RESPECT TO TWO DIFFERENT METRICS

Let (M, g) be a Riemannian manifold and T M be its tangent bundle. The purpose of this paper is to study statistical structures on T M with respect to the metrics Gf1=c g +v (fg) and Gf2=s gf +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 gf is a metric obtained by rescaling the Sasaki metric by a smooth function f andh g is the horizontal lift of g. Moreover, we give some results about Killing vector fields on T M with respect to these metrics. © 2023 Ankara University Mathematics and Statistics.