Special anisotropic conformal changes of conic pseudo-Finsler surfaces
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913864360132608 |
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| author | Youssef, Nabil L. Taha, Ebtsam H. Kotb, A. A. Elgendi, S. G. |
| author_facet | Youssef, Nabil L. Taha, Ebtsam H. Kotb, A. A. Elgendi, S. G. |
| contents | This study presents many special anisotropic conformal changes of a conic pseudo-Finsler surface $(M,F)$, such as $C$-anisotropic and horizontal $C$-anisotropic conformal transformations, which reduce to $C$-conformal when the conformal factor is solely position-dependent. Furthermore, we present vertical $C$-anisotropic conformal changes and demonstrate that they are characterized by the property of $(M,F)$ being Riemannian. Additionally, we examine the anisotropic conformal transformation that fulfils the $ϕT$-condition, the horizontal $ϕT$-condition, and the vertical $ϕT$-condition. The first two conditions reduce to the $\boldsymbolσ T$-condition when the conformal factor relies solely on a positional variable. We demonstrate that, under the vertical $ϕT$-condition change, every Landsberg surface is Berwaldian. Thus, the vertical $ϕT$-condition is equivalent to the $T$-condition. Furthermore, we examine the scenario when the anisotropic conformal factor becomes the main scalar of the non-Riemannian surface $(M,F)$. We present an example of a Finslerian Schwarzschild-de Sitter solution having Finslerian spherical symmetry and apply our results to it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Special anisotropic conformal changes of conic pseudo-Finsler surfaces Youssef, Nabil L. Taha, Ebtsam H. Kotb, A. A. Elgendi, S. G. Differential Geometry 53B40, 53C60 This study presents many special anisotropic conformal changes of a conic pseudo-Finsler surface $(M,F)$, such as $C$-anisotropic and horizontal $C$-anisotropic conformal transformations, which reduce to $C$-conformal when the conformal factor is solely position-dependent. Furthermore, we present vertical $C$-anisotropic conformal changes and demonstrate that they are characterized by the property of $(M,F)$ being Riemannian. Additionally, we examine the anisotropic conformal transformation that fulfils the $ϕT$-condition, the horizontal $ϕT$-condition, and the vertical $ϕT$-condition. The first two conditions reduce to the $\boldsymbolσ T$-condition when the conformal factor relies solely on a positional variable. We demonstrate that, under the vertical $ϕT$-condition change, every Landsberg surface is Berwaldian. Thus, the vertical $ϕT$-condition is equivalent to the $T$-condition. Furthermore, we examine the scenario when the anisotropic conformal factor becomes the main scalar of the non-Riemannian surface $(M,F)$. We present an example of a Finslerian Schwarzschild-de Sitter solution having Finslerian spherical symmetry and apply our results to it. |
| title | Special anisotropic conformal changes of conic pseudo-Finsler surfaces |
| topic | Differential Geometry 53B40, 53C60 |
| url | https://arxiv.org/abs/2505.22593 |