On a new class of Finsler metrics
On a new class of Finsler metrics
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DOI：
10.1016/j.difgeo.2010.12.009
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发表时间：
2011-03
影响因子：
0.5
通讯作者：
Changtao Yu;Hongmei Zhu
中科院分区：
文献类型：
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作者：
Changtao Yu;Hongmei Zhu
本文阐明了（α，β）-模的几何意义。在此基础上，引入了一类新的Finsler度量，称为广义（α，β）-度量，它由一个黎曼度量和一个1-形式定义.这些度量不仅自然地推广了（α，β）-度量，而且还包含了R构造的度量.布莱恩特给出了几类广义（α，β）-度量的喷雾系数公式，并讨论了它们的射影平坦性。
In this paper, the geometric meaning of (α,β)-norms is made clear. On this basis, a new class of Finsler metrics called general (α,β)-metrics are introduced, which are defined by a Riemannian metric and a 1-form. These metrics not only generalize (α,β)-metrics naturally, but also include some metrics structured by R. Bryant. The spray coefficients formula of some kinds of general (α,β)-metrics is given and the projective flatness is also discussed.