Math @ Duke

Publications [#355195] of Robert Bryant
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 Bryant, RL; Foulon, P; Ivanov, SV; Matveev, VS; Ziller, W, Geodesic behavior for Finsler metrics of constant positive flag curvature on S^{2},
Journal of Differential Geometry, vol. 117 no. 1
(January, 2021),
pp. 122 [doi]
(last updated on 2021/05/10)
Abstract: We study nonreversible Finsler metrics with constant flag curvature 1 on S2 and show that the geodesic flow of every such metric is conjugate to that of one of Katok's examples, which form a 1 parameter family. In particular, the length of the shortest closed geodesic is a complete invariant of the geodesic flow. We also show, in any dimension, that the geodesic flow of a Finsler metric with constant positive flag curvature is completely integrable. Finally, we give an example of a Finsler metric on S with positive flag curvature such that no two closed geodesics intersect and show that this is not possible when the metric is reversible or has constant flag curvature. 2


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