In this paper, we show that every homogeneous Finsler metric is a weakly stretch metric if and only if it reduces to a weakly Landsberg metric. This yields an extension of Tayebi–Najafi’s result that proved the result for the class of stretch Finsler metrics. Let \(F:=\alpha \phi (\beta /\alpha )\) be a homogeneous weakly stretch \((\alpha ,\beta )\)-metric on a manifold M. We show that if \(\phi \) is of polynomial type, then F is a Berwald metric. Also, we prove that F is a Berwald metric if and only if it has vanishing S-curvature. Then, we show that F is a Douglas metric if and only if it reduces to a Berwald metric. In continue, we show that every homogenous weakly stretch surface is a Landsberg surface. Finally, we characterize homogeneous weakly stretch spherically symmetric Finsler metrics.

在本文中，我们表明，当且仅当将其简化为弱Landsberg度量时，每个齐次Finsler度量才是弱拉伸度量。这产生了Tayebi–Najafi结果的扩展，证明了扩展Finsler指标类别的结果。令\（F：= \ alpha \ phi（\ beta / \ alpha）\）为流形M上的均质弱拉伸\（（\ alpha，\ beta）\） -度量。我们证明，如果\（\ phi \）是多项式类型，则F是Berwald度量。而且，我们证明F是Berwald度量，当且仅当它具有消失的S曲率。然后，我们证明F当且仅当它减少为Berwald度量时，才是Douglas度量。接下来，我们显示每个均匀的弱拉伸表面都是Landsberg表面。最后，我们描述了均质的弱拉伸球对称Finsler度量。