Finsler Metrics with K=0 and S=0

Details Finsler Metrics with K=0 and S=0 Finsler Metrics with K=0 and S=0

2001-09-10

arxiv.org/abs/math/0109060v1

Mathematics

Differential Geometry

20 pages with three illustrations, latex file using texdraw.sty; Find related papers at http://www.math.iupui.edu/~zshen/index

Scientific paper

In Finsler geometry, there are infinitely many models of constant curvature. The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are projectively flat with non-zero constant curvature. A recent example constructed by the author is projectively flat with zero curvature. In this paper, we introduce a technique to construct non-projectively flat Finsler metrics with zero curvature in each dimension. The technique can be used to construct many non-projectively flat Finsler metrics of constant curvature.

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