Vanishing S-curvature of Randers spaces

TL;DR

This paper characterizes when a Randers space admits a measure with zero Shen's S-curvature, showing such a measure aligns with the Busemann-Hausdorff measure up to a constant.

Contribution

It provides a necessary and sufficient condition for the existence of a measure with vanishing Shen's S-curvature in Randers spaces, linking it to the Busemann-Hausdorff measure.

Findings

Characterization of Randers spaces with zero Shen's S-curvature

Identification of the measure as the Busemann-Hausdorff measure up to a constant

Necessary and sufficient condition for the existence of such a measure

Abstract

We give a necessary and sufficient condition on a Randers space for the existence of a measure for which Shen's S-curvature vanishes everywhere. Moreover, such a measure coincides with the Busemann-Hausdorff measure up to a constant multiplication.