On Randers spaces of constant flag curvature

Journal Article (Journal Article)

This paper concerns a ubiquitous class of Finsler metrics on smooth manifolds of dimension n. These are the Randers metrics. They figure prominently in both the theory and the applications of Finsler geometry. For n ≥ 3, we consider only those with constant flag curvature. For n = 2, we focus on those whose flag curvature is a (possibly constant) function of position only. We characterize such metrics by three efficient conditions. With the help of examples in 2 and 3 dimensions, we deduce that the Yasuda-Shimada classification of Randers space forms actually addresses only a special case. The corrected classification for that special case is sharp, holds for n ≥ 2, and follows readily from our three necessary and sufficient conditions.

Full Text

Duke Authors

Cited Authors

  • Bao, D; Robles, C

Published Date

  • January 1, 2003

Published In

Volume / Issue

  • 51 / 1

Start / End Page

  • 9 - 42

International Standard Serial Number (ISSN)

  • 0034-4877

Digital Object Identifier (DOI)

  • 10.1016/S0034-4877(03)80002-2

Citation Source

  • Scopus