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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
Article
  • 77 Downloads

Abstract

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 

Notes

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Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), 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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