On a Class of Singular Projectively Flat Finsler Metrics with Constant Flag Curvature

Guojun Yang

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arXiv · 1302.3303

On a Class of Singular Projectively Flat Finsler Metrics with Constant Flag Curvature

Guojun Yang

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Abstract

Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we classify a class of singular $(\alpha,\beta)$-metrics which are locally projectively flat with constant flag curvature in dimension $n= 2$ and $n \ge 3$ respectively. Further, we determine the local structure of $m$-Kropina metrics and particularly Kropina metrics which are projectively flat with constant flag curvature and prove that such metrics must be locally Minkowskian but are not necessarily flat-parallel.

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Guojun Yang. 2013-02-14. On a Class of Singular Projectively Flat Finsler Metrics with Constant Flag Curvature. https://arxiv.org/abs/1302.3303

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