Killing frames and S-curvature of homogeneous Finsler spaces

TL;DR

This paper derives a formula for S-curvature in homogeneous Finsler spaces using Killing vector fields, establishes conditions for isotropic S-curvature, and provides explicit formulas for Randers spaces, advancing understanding of curvature properties.

Contribution

It introduces a new formula for S-curvature in homogeneous Finsler spaces and characterizes isotropic S-curvature in terms of vanishing S-curvature, including explicit results for Randers spaces.

Findings

Homogeneous Finsler spaces have isotropic S-curvature iff S-curvature vanishes.

Derived a formula for S-curvature involving Killing vector fields.

Explicit S-curvature formula for Randers spaces matching previous results.

Abstract

In this paper, we first deduce a formula of S-curvature of homogeneous Finsler spaces in terms of Killing vector fields. Then we prove that a homogeneous Finsler space has isotropic S-curvature if and only if it has vanishing S-curvature. In the special case that the homogeneous Finsler space is a Randers space, we give an explicit formula which coincides with the previous formula obtained by the second author using other methods.