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We describe the    $$(\alpha ,\beta )$$  ( α , β ) -metrics whose the  T -tensor vanishes ( T -condition) and the    $$(\alpha ,\beta )$$  ( α , β ) -metrics that satisfy the    $$\sigma T$$  σ T -condition    $$\sigma _hT^h_{ijk}=0$$  σ h T ijk h = 0 , where    $$\sigma _h=\frac{\partial \sigma }{\partial x^h}$$  σ h = ∂ σ ∂ x h and    $$\sigma $$  σ is a smooth function on  M . These classes have already been obtained by Shen and Asanov in a completely different approach. The Finsler metrics of the first class are Berwaldian, the metrics of the second class are almost regular non-Berwaldian Landsberg metrics.

$$(\alpha ,\beta )$$-Metrics Satisfying the T-Condition or the $$\sigma T$$-Condition