Two-dimensional Finsler metrics of constant curvature

Details Two-dimensional Finsler metrics of constant curvature Two-dimensional Finsler metrics of constant curvature

2001-09-15

arxiv.org/abs/math/0109097v1

Mathematics

Differential Geometry

17 pages, 2 figures, latex file using texdraw

Scientific paper

A 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.

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