Publications [#318264] of Robert Bryant

Papers Published

1. Bryant, RL, GEODESICALLY REVERSIBLE FINSLER 2-SPHERES OF CONSTANT CURVATURE, in Nankai Tracts in Mathematics, Nankai Tracts in Mathematics, edited by Griffiths, PA, vol. 11 (Winter, 2006), pp. 95-111, WORLD SCIENTIFIC, ISBN 9789812700612 [math.DG/0407514], [doi]
   (last updated on 2025/02/21)

   Abstract:
   A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long- standing problem in Finsler geometry.