On the Flag Curvature of Finsler Metrics of Scalar Curvature
On the Flag Curvature of Finsler Metrics of Scalar Curvature
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DOI：
10.1112/s0024610703004599
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发表时间：
2003-03
期刊：
影响因子：
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通讯作者：
Xinyue Chen;X. Mo;Z. Shen
中科院分区：
文献类型：
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作者：
Xinyue Chen;X. Mo;Z. Shen
Finsler度量的旗曲率称为黎曼量，因为它是黎曼几何中截面曲率的推广。在Finsler几何中，有几个非黎曼量，如(平均)Cartan挠率、(平均)Landsberg曲率和S曲率，这些量在黎曼度量下都消失了。理解这些量的几何意义是很重要的。本文研究了标量曲率(即旗曲率是狭缝切丛上的标量函数)的Finsler度量，当某些非黎曼量是各向同性时，部分地确定了旗曲率。利用得到的旗曲率公式，对具有各向同性S曲率的局部射影平坦Randers度量进行了分类。
The flag curvature of a Finsler metric is called a Riemannian quantity because it is an extension of sectional curvature in Riemannian geometry. In Finsler geometry, there are several non‐Riemannian quantities such as the (mean) Cartan torsion, the (mean) Landsberg curvature and the S‐curvature, which all vanish for Riemannian metrics. It is important to understand the geometric meanings of these quantities. In the paper, Finsler metrics of scalar curvature (that is, the flag curvature is a scalar function on the slit tangent bundle) are studied and the flag curvature is partially determined when certain non‐Riemannian quantities are isotropic. Using the obtained formula for the flag curvature, locally projectively flat Randers metrics with isotropic S‐curvature are classified.