Randers Metrics of Isotropic S-Curvature

  • Xinyue Cheng
  • Zhongmin Shen


There are several important geometric quantities in Finsler geometry. The Cartan torsion C is a primary quantity. There is another quantity which is determined by the Busemann-Hausdorff volume form, that is the so-called distortion τ. The vertical differential of τ on each tangent space gives rise to the mean Cartan torsion \( I: = \tau _{y^k } dx^k \). C, τ and I are the basic non-Riemannian geometric quantities which characterize Riemann metrics among Finsler metrics and are connected each other as (1.17) and (1.18). In this chapter, we are going to introduce a new quantity which is defined as a rate of change of the distortion along a geodesic.


Scalar Function Volume Form Constant Sectional Curvature Finsler Geometry Finsler Metrics 
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Copyright information

© Science Press Beijing and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Xinyue Cheng
    • 1
  • Zhongmin Shen
    • 2
  1. 1.School of Mathematics and StatisticsChongqing University of TechnologyLijiatuo, ChongqingChina
  2. 2.Department of Mathematical SciencesIndiana University-Purdue University Indianapolis (IUPUI)IndianapolisUSA

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