Projectively Flat Randers Metrics

  • Xinyue Cheng
  • Zhongmin Shen


According to the Beltrami theorem in Riemann geometry, a Riemann metric is locally projectively flat if and only if it is of constant sectional curvature.


Open Subset Finsler Space Unit Speed Constant Sectional Curvature Finsler Geometry 
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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  1. [AZ]
    H. Akbar-Zadeh, Sur les espaces de Finsler á courbures sectionnelles constantes, Bull. Acad. Roy. Bel. Cl, Sci, 5e Série-Tome LXXXIV(1988),281–322.MathSciNetGoogle Scholar
  2. [BaMa]
    S. Bácsó and M. Matsumoto, On Finsler spaces of Douglas type II. Projectively flat spaces, Publ. Math. Debrecen, 53(1998), 423–438.MathSciNetzbMATHGoogle Scholar
  3. [ChMoSh]
    X. Chen(g), X. Mo and Z. Shen, On the flag curvature of Finsler metrics of scalar curvature, Journal of the London Mathematical Society, 68(2)(2003), 762–780.MathSciNetGoogle Scholar
  4. [Sh1]
    Z. Shen, Projectively flat Randers metrics of constant flag curvature, Math. Ann., 325(2003), 19–30.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [Sh2]
    Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, 2001.Google Scholar
  6. [Sh3]
    Z. Shen, Lectures on Finsler Geometry, World Scientific Publishers, 2001.Google Scholar

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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