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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关于Finsler几何中的一类拉伸度量

拉伸指标的类别包含Landsberg指标的类别和R-二次方的指标。在本文中，我们证明，当且仅当它是Berwaldian时，带有消失的S曲率的正则非Randers类型\（（\ alpha，\ beta）\） -度量是可拉伸的。令F为几乎规则的非Randers类型\（（\ alpha，\ beta）\） -metric。假设F不是Berwald度量。然后，我们找到了不是Landsbergian的一系列拉伸\（（\ alpha，\ beta）\）-度量。通过举一个例子，我们表明上述事实不适用于兰德斯类型的度量标准。因此，每个常规\（（（\ alpha，\ beta）\）当且仅当它是Berwald度量时，具有各向同性S曲率的R二次方才是R二次方。