Geodesically reversible Finsler 2-spheres of constant curvature

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dc.creatorBryant, Robert L.
dc.date2004-07-29
dc.date2004-08-02
dc.date.accessioned2026-07-07T08:51:45Z
dc.date.available2026-07-07T08:51:45Z
dc.descriptionA 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.
dc.description11 pages, references added, some arguments improved and exposition rearranged
dc.identifierhttps://arxiv.org/abs/math/0407514
dc.identifierhttp://arxiv.org/abs/math/0407514
dc.identifierInspired by S. S. Chern--A Memorial Volume in Honor of a Great Mathematician, Nankai Tracts in Mathematics, edited by P. A. Griffiths, vol. 11 (Winter, 2006), World Scientific
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145043
dc.subjectDifferential Geometry
dc.subject53C60, 53B40
dc.titleGeodesically reversible Finsler 2-spheres of constant curvature
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