Projectively flat Finsler metrics of constant flag curvature
Projectively flat Finsler metrics of constant flag curvature
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DOI：
10.1090/s0002-9947-02-03216-6
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发表时间：
2002-12
影响因子：
1.3
通讯作者：
Z. Shen
中科院分区：
文献类型：
--
作者：
Z. Shen
Finsler度量的开子集在R n与直测地线被称为是投射。已知任何射影芬斯勒度量的旗曲率是切向量的标量函数（如果它是黎曼的，则旗曲率必须是常数）。本文讨论了常旗曲率的射影Finsler度量的分类问题。我们用泰勒展开式或代数公式来表示它们。本文构造的许多例子可以作为Finsler几何中的模型。
Finsler metrics on an open subset in R n with straight geodesics are said to be projective. It is known that the flag curvature of any projective Finsler metric is a scalar function of tangent vectors (the flag curvature must be a constant if it is Riemannian). In this paper, we discuss the classification problem on projective Finsler metrics of constant flag curvature. We express them by a Taylor expansion or an algebraic formula. Many examples constructed in this paper can be used as models in Finsler geometry.