Arabian Journal of Mathematics

, Volume 8, Issue 2, pp 153–160 | Cite as

On a class of stretch metrics in Finsler Geometry

  • Akbar TayebiEmail author
  • Hassan Sadeghi
Open Access


The class of stretch metrics contains the class of Landsberg metrics and the class of R-quadratic metrics. In this paper, we show that a regular non-Randers type \((\alpha , \beta )\)-metric with vanishing S-curvature is stretchian if and only if it is Berwaldian. Let F be an almost regular non-Randers type \((\alpha , \beta )\)-metric. Suppose that F is not a Berwald metric. Then, we find a family of stretch \((\alpha , \beta )\)-metrics which is not Landsbergian. By presenting an example, we show that the mentioned facts do not hold for the Randers-type metrics. It follows that every regular \((\alpha , \beta )\)-metric with isotropic S-curvature is R-quadratic if and only if it is a Berwald metric.

Mathematics Subject Classification

53C60 53C25 



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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of QomQomIran

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