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Finsler Metrics with K=0 and S=0

Zhongmin Shen
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Abstract

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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Zhongmin Shen. 2001-09-10. Finsler Metrics with K=0 and S=0. https://arxiv.org/abs/math/0109060

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