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Randers Metrics of Isotropic S-Curvature

  • Xinyue Cheng
  • Zhongmin Shen

Abstract

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.

Keywords

Scalar Function Volume Form Constant Sectional Curvature Finsler Geometry Finsler Metrics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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