On a class of locally projectively flat Finsler metrics
On a class of locally projectively flat Finsler metrics
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DOI：
10.1142/s0129167x1650052x
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发表时间：
2016-06
影响因子：
0.6
通讯作者：
Benling Li;Z. Shen
中科院分区：
文献类型：
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作者：
Benling Li;Z. Shen
局部射影平坦Finsler度量是Finsler几何中的一组重要度量.这些度量的特征是希尔伯特第四问题的常规情况。本文研究一类由Riemann度量α = aij（x）yiyj和1-形式β = bi（x）yi构成的Finsler度量，称之为广义（α，β）-度量.当α是射影平坦的时，我们对那些局部射影平坦的进行分类.通过求解相应的非线性偏微分方程，完全确定了这类度量。然后找到了一组新的局部射影平坦Finsler度量。
Locally projectively flat Finsler metrics compose an important group of metrics in Finsler geometry. The characterization of these metrics is the regular case of the Hilbert’s Fourth Problem. In this paper, we study a class of Finsler metrics composed by a Riemann metric α = aij (x)yi yj and a 1-form β = bi(x)yi called general (α, β)-metrics. We classify those locally 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 locally projectively flat Finsler metrics is found.