Two-dimensional Finsler metrics of constant curvature

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dc.creatorShen, Zhongmin
dc.date2001-09-15
dc.date.accessioned2026-07-07T04:43:23Z
dc.date.available2026-07-07T04:43:23Z
dc.descriptionA Riemannian metric is of constant curvature if and only if it is locally projectively flat. There are infinitely many locally projectively flat Finsler metrics of constant curvature, that are special solutions to the Hilbert's Fourth Problem. In this paper, we use the technique in the paper titled "Finsler metrics with K=0 and S=0" (math.DG/0109060) to construct infinitely many Finsler metrics on the 2-sphere with constant curvature K=1 and infinitely many Finsler metrics on the 2-disk with constant curvature K = -1. These metrics are not projectively flat. So far, the classification of Finsler metrics of constant curvature has not been completely done yet. These examples are important to the classification problem.
dc.description17 pages, 2 figures, latex file using texdraw
dc.identifierhttps://arxiv.org/abs/math/0109097
dc.identifierhttp://arxiv.org/abs/math/0109097
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62197
dc.subjectDifferential Geometry
dc.subjectMetric Geometry
dc.subject53C60; 53B40
dc.titleTwo-dimensional Finsler metrics of constant curvature
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