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Randers Metrics of Weakly Isotropic Flag Curvature

  • Xinyue Cheng
  • Zhongmin Shen

Abstract

It is still an open problem to classify Randers metrics of scalar flag curvature. However, if the flag curvature is weakly isotropic, one can determine the local metric structure. By definition, a Randers metric F = α+β on an n-dimensional manifold M is of weakly isotropic flag curvature if its flag curvature is a scalar function on TM in the following form:
$$ K = \frac{{3\theta }} {F} + \sigma , $$
(7.1)
where θ = t i (x)y i is a 1-form and σ = σ(x) is a scalar function on M. The main method is to express a Randers metric F = α + β using navigation data (h, W). This method can be also used to investigate weak Einstein Randers metrics.

Keywords

Scalar Function Sectional Curvature Local Coordinate System Ricci Curvature Finsler Space 
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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