On natural symmetries on slit tangent bundles of Finsler manifolds

TL;DR

This paper introduces a new class of metrics called F-natural metrics on the slit tangent bundle of Finsler manifolds, generalizing g-natural metrics from Riemannian geometry, and characterizes associated symmetries such as conformal and Killing vector fields.

Contribution

It defines F-natural metrics on slit tangent bundles of Finsler manifolds and characterizes their conformal, homothetic, and Killing vector fields, extending known concepts from Riemannian geometry.

Findings

Defined F-natural metrics using six real functions.

Characterized conformal vector fields on slit tangent bundles.

Extended symmetry analysis to Finsler geometric context.

Abstract

In this paper, we introduce a broad class of metrics on the slit tangent bundle of Finsler manifolds, termed \emph{$F$-natural metrics}. These metrics parallel the well-established $g$-natural metrics on the tangent bundles of Riemannian manifolds and are constructed using six real functions defined over the domain of positive real numbers. We provide an in-depth characterization of conformal, homothetic, and Killing vector fields derived from specific lifts of vector fields and tensor sections on the slit tangent bundle, which is equipped with a general pseudo-Riemannian $F$-natural metric.