$(\alpha,\beta)$-metrics satisfying the $T$-Condition or the $\sigma T$-Condition

We describe the $(α, β)$ -metrics whose the $T$ -tensor vanishes ( $T$ -condition) and the $(α, β)$ -metrics that satisfy the $\sigma T $- c o n d i t i o n$ \sigma_hT^h_{ijk}=0 $, w h e r e$ \sigma_h=\frac{\partial \sigma}{\partial x^h} $a n d$ \sigma $i s a s m o o t h f u n c t i o n o n$ M$. These classes have already been obtained by Z. Shen and G. S. 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.

$(α, β)$ -metrics satisfying the $T$ -Condition or the $σ T$ -Condition

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$(α, β)$ -metrics satisfying the $T$ -Condition or the $σ T$ -Condition

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(α,β)(α,β)-metrics satisfying the TT-Condition or the σTσT-Condition

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(α,β)(α,β)-metrics satisfying the TT-Condition or the σTσT-Condition

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|讲解博客

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$(α, β)$ -metrics satisfying the $T$ -Condition or the $σ T$ -Condition

讲解博客

AI智能校验

$(α, β)$ -metrics satisfying the $T$ -Condition or the $σ T$ -Condition

讲解博客

AI智能校验