The T-tensor of spherically symmetric Finsler metrics

Salah G. Elgendi

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arXiv · 2601.16021

The T-tensor of spherically symmetric Finsler metrics

Salah G. Elgendi

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Abstract

This paper is devoted to the study of the T-tensor associated with a spherically symmetric Finsler metric $F=u\phi(r,s)$ on $\mathbb{R}^n$. We derive a general expression for the T-tensor in terms of the scalar function $\phi(r, s)$ and its partial derivatives. Furthermore, we characterize all spherically symmetric Finsler metrics satisfying the so-called T-condition, that is, those for which the T-tensor vanishes. In addition, we obtain the formula for the mean Cartan tensor and demonstrate that all spherically symmetric Finsler metrics of dimension $n \geq 3$, with a non-zero mean Cartan tensor are quasi-C-reducible.

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Salah G. Elgendi. 2026-01-22. The T-tensor of spherically symmetric Finsler metrics. https://arxiv.org/abs/2601.16021

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