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Geodesic behavior for Finsler metrics of constant positive flag curvature on S^2

dc.contributor.author Bryant, R
dc.contributor.author Foulon, P
dc.contributor.author Ivanov, S
dc.contributor.author Matveev, VS
dc.contributor.author Ziller, W
dc.date.accessioned 2020-05-01T13:30:53Z
dc.date.available 2020-05-01T13:30:53Z
dc.identifier.uri https://hdl.handle.net/10161/20574
dc.description.abstract 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
dc.publisher International Press of Boston
dc.relation.ispartof Journal of Differential Geometry
dc.subject Finsler geometry
dc.subject Geodesic flow
dc.title Geodesic behavior for Finsler metrics of constant positive flag curvature on S^2
dc.type Journal article
duke.contributor.id Bryant, R|0110365
dc.date.updated 2020-05-01T13:30:53Z
pubs.organisational-group Trinity College of Arts & Sciences
pubs.organisational-group Mathematics
pubs.organisational-group Duke
pubs.publication-status Accepted
duke.contributor.orcid Bryant, R|0000-0002-4890-2471


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