A generalization and short proof of a theorem of Hano on affine vector fields

TL;DR

This paper proves that bounded affine vector fields on complete Finsler manifolds are Killing vector fields, generalizing Hano's Riemannian result with a simpler proof.

Contribution

It extends Hano's theorem from Riemannian to Finsler manifolds and provides a more straightforward proof.

Findings

Bounded affine vector fields are Killing vector fields on complete Finsler manifolds

The result generalizes Hano's theorem from Riemannian to Finsler geometry

The proof is significantly simpler than previous methods

Abstract

We prove that a bounded affine vector field on a complete Finsler manifold is a Killing vector field. This generalizes the analogous result of Hano for Riemannian manifolds. Even though our result is more general, the proof is significantly simpler.