2025/05/28 by Youssef, Nabil L., Taha, Ebtsam H., Kotb, A. A. +1
#53B40 #53C60 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2505.22593
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.