Publications [#243403] of Robert Bryant

Papers Published

  1. Bryant, RL, Projectively flat Finsler 2-spheres of constant curvature, Selecta Math. (N.S.), vol. 3 no. 2 (1997), pp. 161-203
    (last updated on 2017/12/14)

    Author's Comments:
    This paper might be regarded as a sequel to the previous one. In it, I prove that, up to diffeomorphism, there is a 2-parameter family of Finsler metrics on the standard 2-sphere whose geodesics are the great circles and whose Finsler-Gauss curvature is identically 1. Explicit formulas for these Finsler metrics are established and it is shown that the only symmetric Finsler metrics with this property are the known Riemannian ones. The introduction contains a discussion of the relation of these results with Hilbert's Fourth Problem.