On natural symmetries on slit tangent bundles of Finsler manifolds

Abstract

In this paper, we introduce a broad class of metrics on the slit tangent bundle of Finsler manifolds, referred to as F-natural metrics. These metrics are analogous to the well-established g-natural metrics on tangent bundles of Riemannian manifolds and are defined by six real functions on the domain of positive real numbers. We present an in-depth analysis of conformal, homothetic, and Killing vector fields associated with specific lifts of vector fields and tensor sections on the slit tangent bundle, equipped with a general pseudo-Riemannian F-natural metric. Notably, we prove that the geodesic vector field cannot be conformal and that, with respect to certain families of F-natural metrics, the Liouville vector field can indeed be conformal, homothetic, or Killing on the slit tangent bundle.