Finsler surfaces with vanishing $T$-tensor
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914656359022592 |
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| author | Elgendi, Salah G. |
| author_facet | Elgendi, Salah G. |
| contents | In this paper, for Finsler surfaces, we prove that the T-condition and $σT$-condition coincide. For higher dimensions $n\geq 3$, we illustrate by an example that the T-condition and $σT$-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 $σT$-condition is satisfied. By solving the Landsberg's PDE, we classify all Finsler surfaces satisfying the T-condition, or equivalently the $σT$-condition. Some examples are provided and studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finsler surfaces with vanishing $T$-tensor Elgendi, Salah G. Differential Geometry 53C60, 53B40 In this paper, for Finsler surfaces, we prove that the T-condition and $σT$-condition coincide. For higher dimensions $n\geq 3$, we illustrate by an example that the T-condition and $σT$-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 $σT$-condition is satisfied. By solving the Landsberg's PDE, we classify all Finsler surfaces satisfying the T-condition, or equivalently the $σT$-condition. Some examples are provided and studied. |
| title | Finsler surfaces with vanishing $T$-tensor |
| topic | Differential Geometry 53C60, 53B40 |
| url | https://arxiv.org/abs/2401.15873 |