Periodica Mathematica Hungarica

, Volume 67, Issue 2, pp 155–166 | Cite as

On a class of projectively flat Finsler metrics with weakly isotropic flag curvature

  • Guangzu Chen
  • Xinyue Cheng
  • Mingao Yuan


In this paper, we study a class of Finsler metrics defined by a Riemannian metric and 1-form. We classify those metrics which are projectively flat with weakly isotropic flag curvature.

Key words and phrases

projectively flat Finsler metric (α, β)-metric the flag curvature 

Mathematics subject classification number

53B40 53C60 


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  1. [1]
    L. Berwald, Über die n-dimensionalen Geometrien characteristic konstanter Krümmung, in denen die Geraden die kürzesten sind, Math. Z., 30 (1929), 449–469 (in German).MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    L. Berwald, Über eine characteristic Eigenschaft der allgemenin Räume konstanter Krümmung mit gradlinigen Extremalen, Monatsh. Math. Phys., 36 (1929), 315–330 (in German).MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    S. S. Chern and Z. Shen, Riemann-Finsler Geometry, Nankai Tracts in Mathematics 6, World Scientific, 2005.Google Scholar
  4. [4]
    D. Hilbert, Mathematical problems, Bull. Amer. Math. Soc. (N.S.), 37 (2000), 407–436; Reprinted from Bull. Amer. Math. Soc. (N.S.), 8 (July 1902), 437–479.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    R. S. Ingarden, On the geometrically absolute optical representation in the electron microscope, Trav. Soc. Sci. Lettr. Wroclaw, B45 (1957), 3–60.Google Scholar
  6. [6]
    B. Li and Z. Shen, On a class of projectively flat Finsler metrics with constant flag curvature, Internat. J. Math., 18 (2007), 749–760.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    X. Mo, Z. Shen and C. Yang, Some constructions of projectively flat Finsler metrics, Sci. China, Ser. A, 49 (2006), 703–714.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    B. Najafi, Z. Shen and A. Tayebi, Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties, Geom. Dedicata, 131 (2008), 87–97.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    Z. Shen, On projectively flat Randers metrics of constant flag curvature, Math. Ann., 325 (2003), 19–30.MathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    Z. Shen and G. C. Yildirim, On a class of projectively flat metrics with constant flag curvature, Canad. J. Math., 60 (2008), 443–456.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Z. Shen, Lectures on Finsler geometry, World Scientific Publishers, Singapure, 2001.CrossRefMATHGoogle Scholar
  12. [12]
    Z. Shen, On projectively flat (α, β)-metric, Canad. Math. Bull., 52 (2009), 132–144.MathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    Z. Shen, Projectively flat Finsler metrics of constant flag curvature, Trans. Amer. Math. Soc., 355 (2003), 1713–1728.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2013

Authors and Affiliations

  1. 1.Department of MathematicsTongji UniversityShanghaiP.R. China
  2. 2.School of Mathematics and StatisticsChongqing University of TechnologyChongqingP.R. China

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