Special Anisotropic Conformal Changes of Conic Pseudo-Finsler Surfaces

Résumé

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 σT-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.

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