The T-tensor of spherically symmetric Finsler metrics
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909997937459200 |
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| author | Elgendi, Salah G. |
| author_facet | Elgendi, Salah G. |
| contents | This paper is devoted to the study of the T-tensor associated with a spherically symmetric Finsler metric $F=uϕ(r,s)$ on \(\mathbb{R}^n\). We derive a general expression for the T-tensor in terms of the scalar function \(ϕ(r, s)\) 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The T-tensor of spherically symmetric Finsler metrics Elgendi, Salah G. Differential Geometry 53B40, 53C60 This paper is devoted to the study of the T-tensor associated with a spherically symmetric Finsler metric $F=uϕ(r,s)$ on \(\mathbb{R}^n\). We derive a general expression for the T-tensor in terms of the scalar function \(ϕ(r, s)\) 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. |
| title | The T-tensor of spherically symmetric Finsler metrics |
| topic | Differential Geometry 53B40, 53C60 |
| url | https://arxiv.org/abs/2601.16021 |