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arXiv · 1510.06303

On a class of projectively flat Finsler metrics

Benling Li·Zhongmin Shen
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Abstract

In this paper, we study a class of Finsler metrics composed by a Riemann metric $α=\sqrt{a_{ij}(x)y^i y^j}$ and a $1$-form $β=b_i(x)y^i$ called general ($α$, $β$)-metrics. We classify those projectively flat when $α$ is projectively flat. By solving the corresponding nonlinear PDEs, the metrics in this class are totally determined. Then a new group of projectively flat Finsler metrics is found.

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Benling Li, Zhongmin Shen. 2015-10-21. On a class of projectively flat Finsler metrics. https://arxiv.org/abs/1510.06303

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