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Geodesic behavior for Finsler metrics of constant positive flag curvature on \(S^2\). (English) Zbl 1486.53086

The paper under review deals with the study of Finsler metrics of constant positive flag curvature on \(S^2\). Some interesting results for Finsler metrics on \(S^2\) with constant flag curvature 1 are obtained. A complete classification of the geodesic flows of Finsler metrics on \(S^2\) with constant flag curvature is given. Important results in dimensions \(n\geq 2\) are found.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C22 Geodesics in global differential geometry
53D25 Geodesic flows in symplectic geometry and contact geometry
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References:

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