Publications [#302461] of Colleen M Robles

Papers Published

1. Bao, D; Robles, C, On Randers spaces of constant flag curvature, Reports on Mathematical Physics, vol. 51 no. 1 (January, 2003), pp. 9-42, Elsevier BV, ISSN 0034-4877 [doi]
   (last updated on 2026/01/17)

   Abstract:
   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.