Dually Flat Randers Metrics

  • Xinyue Cheng
  • Zhongmin Shen


The notion of dually flat metrics was first introduced by Amari and Nagaoka ([AmNa]) when they study the information geometry on Riemann spaces. Later on, Shen extends the notion of dually flatness to Finsler metrics ([Sh]). Locally dually flat Finsler metrics are studied in Finsler information geometry and naturally arise from the investigation on so-called flat information structure.


Open Subset Scalar Function Riemann Space Irreducible Polynomial Finsler Space 
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  1. [Am]
    S.-I. Amari, Differential-Geometrical Methods in Statistics, Springer Lecture Notes in Statistics, 28, Springer-Verlag, Berlin, 1985.zbMATHCrossRefGoogle Scholar
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    S.-I. Amari and H. Nagaoka, Methods of Information Geometry, AMS Translation of Math. Monographs, 191, Oxford University Press, 2000.Google Scholar
  3. [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
  4. [ChSh]
    X. Chen(g) and Z. Shen, Randers metrics with special curvature properties, Osaka Journal of Mathematics, 40(2003), 87–101.MathSciNetGoogle Scholar
  5. [ChShZh]
    X. Cheng, Z. Shen and Y. Zhou, On locally dually flat Finsler metrics, International Journal of Mathematics, 21(11)(2010), 1–13.MathSciNetCrossRefGoogle Scholar
  6. [Sh]
    Z. Shen, Riemann-Finsler geometry with applications to information geometry, Chin. Ann. Math., 27B(1)(2006), 73–94.CrossRefGoogle 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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