Zermelo deformation of Finsler metrics by Killing vector fields

TL;DR

This paper investigates how Zermelo deformation affects geodesics, Jacobi fields, and curvature in Finsler geometry, especially when deformed by Killing vector fields, and shows preservation of local symmetry.

Contribution

It provides new insights into the behavior of Finsler geometric structures under Zermelo deformation involving Killing vector fields, including symmetry preservation.

Findings

Geodesics and curvature are affected in specific ways under Zermelo deformation.

Zermelo deformation preserves local symmetry when applied to locally symmetric Finsler metrics.

The behavior of Jacobi vector fields under deformation is characterized.

Abstract

We show how geodesics, Jacobi vector fields and flag curvature of a Finsler metric behave under Zermelo deformation with respect to a Killing vector field. We also show that Zermelo deformation with respect to a Killing vector field of a locally symmetric Finsler metric is also locally symmetric.