Randers Metrics of Isotropic S-Curvature

Xinyue Cheng () and Zhongmin Shen ()
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Xinyue Cheng: Chongqing University of Technology, School of Mathematics and Statistics
Zhongmin Shen: Indiana University-Purdue University Indianapolis (IUPUI), Department of Mathematical Sciences

Chapter Chapter 3 in Finsler Geometry, 2012, pp 27-49 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-3-642-24888-7_3

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