On projectively flat Kropina metrics

Xiaoling Zhang; Yibing Shen

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arXiv · 1304.1612

On projectively flat Kropina metrics

Xiaoling Zhang·Yibing Shen

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Abstract

In this paper, a characteristic condition of the projectively flat Kropina metric is given. By it, we prove that a Kropina metric $F=\alpha^2/\beta$ with constant curvature $K$ and $\|\beta\|_{\alpha}=1$ is projectively flat if and only if $F$ is locally Minkowskian.

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Xiaoling Zhang, Yibing Shen. 2013-04-05. On projectively flat Kropina metrics. https://arxiv.org/abs/1304.1612

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