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Dually Flat Randers Metrics

  • Xinyue Cheng
  • Zhongmin Shen

Abstract

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.

Keywords

Open Subset Scalar Function Riemann Space Irreducible Polynomial 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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Bibliography

  1. [Am]
    S.-I. Amari, Differential-Geometrical Methods in Statistics, Springer Lecture Notes in Statistics, 28, Springer-Verlag, Berlin, 1985.zbMATHCrossRefGoogle Scholar
  2. [AmNa]
    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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