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On Randers spaces of constant flag curvature

Publication ,  Journal Article
Bao, D; Robles, C
Published in: Reports on Mathematical Physics
January 1, 2003

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.

Duke Scholars

Published In

Reports on Mathematical Physics

DOI

ISSN

0034-4877

Publication Date

January 1, 2003

Volume

51

Issue

1

Start / End Page

9 / 42

Related Subject Headings

  • Mathematical Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Bao, D., & Robles, C. (2003). On Randers spaces of constant flag curvature. Reports on Mathematical Physics, 51(1), 9–42. https://doi.org/10.1016/S0034-4877(03)80002-2
Bao, D., and C. Robles. “On Randers spaces of constant flag curvature.” Reports on Mathematical Physics 51, no. 1 (January 1, 2003): 9–42. https://doi.org/10.1016/S0034-4877(03)80002-2.
Bao D, Robles C. On Randers spaces of constant flag curvature. Reports on Mathematical Physics. 2003 Jan 1;51(1):9–42.
Bao, D., and C. Robles. “On Randers spaces of constant flag curvature.” Reports on Mathematical Physics, vol. 51, no. 1, Jan. 2003, pp. 9–42. Scopus, doi:10.1016/S0034-4877(03)80002-2.
Bao D, Robles C. On Randers spaces of constant flag curvature. Reports on Mathematical Physics. 2003 Jan 1;51(1):9–42.
Journal cover image

Published In

Reports on Mathematical Physics

DOI

ISSN

0034-4877

Publication Date

January 1, 2003

Volume

51

Issue

1

Start / End Page

9 / 42

Related Subject Headings

  • Mathematical Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences