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arXiv · 2401.15873

Finsler surfaces with vanishing $T$-tensor

Salah G. Elgendi
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Abstract

In this paper, for Finsler surfaces, we prove that the T-condition and $\sigma T$-condition coincide. For higher dimensions $n\geq 3$, we illustrate by an example that the T-condition and $\sigma T$-condition are not equivalent. We show that the non-homothetic conformal change of a Berwald (resp. a Landsberg) surface is Berwaldian (resp. Landsbergian) if and only if the $\sigma T$-condition is satisfied. By solving the Landsberg's PDE, we classify all Finsler surfaces satisfying the T-condition, or equivalently the $\sigma T$-condition. Some examples are provided and studied.

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Salah G. Elgendi. 2024-01-29. Finsler surfaces with vanishing $T$-tensor. https://doi.org/10.1016/j.geomphys.2024.105110

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