Browsing by Subject "53C60, 53C22, 52C24"

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    Geodesic behavior for Finsler metrics of constant positive flag curvature on $S^2$
    (2017-11-01) Bryant, RL; Foulon, P; Ivanov, SV; Matveev, VS; Ziller, W
    We study non-reversible Finsler metrics with constant flag curvature 1 on S^2 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 metrics with constant positive flag curvature is completely integrable. Finally, we give an example of a Finsler metric on~$S^2$ with positive flag curvature such that no two closed geodesics intersect and show that this is not possible when the metric is reversible or have constant flag curvature