Some remarks on the geometry of Kropina spaces

TL;DR

This paper explores the geometric properties of Kropina spaces, characterizing special subclasses using vector fields and relating their isometry groups to those of underlying Riemannian spaces.

Contribution

It provides new characterizations of weakly-Berwald and Berwald Kropina spaces via Killing and parallel vector fields, linking their isometry groups to Riemannian isometries.

Findings

Weakly-Berwald Kropina spaces characterized by Killing vector fields W.

Berwald Kropina spaces characterized by parallel vector fields W.

Isometry groups of Kropina spaces coincide locally with Riemannian isometry groups.

Abstract

Using the navigation data (h,W) of a Kropina space, we characterize weakly-Berwald Kropina spaces and Berwald Kropina spaces by means of the Killing vector field W and the parallel vector field W, respectively. Moreover, the local 1-parameter group of Finslerian local isometries of the Kropina space coincides with the local 1-parameter group Riemannian of local isometries on (M, h).