Randers Metrics of Scalar Flag Curvature

Abstract

We study an important class of Finsler metrics, namely, Randers metrics. We classify Randers metrics of scalar flag curvature whose S-curvatures are isotropic. This class of Randers metrics contains all projectively flat Randers metrics with isotropic S-curvature and Randers metrics of constant flag curvature.2000 Mathematics subject classification: primary 53B40; secondary 53C60.

Zermelo navigation and a speed limit to quantum information processing

“…A Randers metric is a Finsler metric that can be cast as the sum of a Riemannian metric and a linear term [26].…”

A class of Finsler metrics with isotropic S-curvature

“…If a Randers metric is of scalar flag curvature, then (1) and (2) are actually equivalent ( [7], [18]). In particular, if a Randers metric is of constant flag curvature, then it must be of constant S-curvature ( [1], [2]).…”

“…In particular, if a Randers metric is of constant flag curvature, then it must be of constant S-curvature ( [1], [2]). We have classified Randers metrics of scalar flag curvature and isotropic S-curvature ( [4], [7]). Further, we have characterized the locally projectively flat Finsler metrics with isotropic S-curvature ( [6]).…”

The spherically symmetric Finsler metrics with isotropic S-curvature

“…This shows the condition of isotropic S-curvature actually is rather relaxed. If imposing of scalar flag curvature and isotropic S-curvature, X. Cheng and Z. Shen completely determined the local structure of Randers metrics [5].…”