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.
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Tayebi, A., Sadeghi, H. On a class of stretch metrics in Finsler Geometry. Arab. J. Math. 8, 153–160 (2019). https://doi.org/10.1007/s40065-018-0216-6
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DOI: https://doi.org/10.1007/s40065-018-0216-6