Conformal vector fields on Finsler manifolds

TL;DR

This paper extends the understanding of conformal and affine vector fields on Finsler manifolds by using tangent bundle geometry and the pull-back formalism, providing new characterizations and implications.

Contribution

It introduces new characterizations of affine and conformal vector fields on spray and Finsler manifolds using advanced geometric tools.

Findings

New characterizations of affine vector fields on spray manifolds.

Enhanced descriptions of conformal vector fields on Finsler manifolds.

Derived consequences for vector fields with these properties on the underlying manifold.

Abstract

Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection ('pull-back formalism'), first we enrich the known lists of the characterizations of affine vector fields on a spray manifold and conformal vector fields on a Finsler manifold. Second, we deduce consequences on vector fields on the underlying manifold of a Finsler structure having one or two of the mentioned geometric properties.