2022/08/07 by S. G. Elgendi, Elgendi, Salah G.
Physics and Astronomy · #53B40 #53C60 #58B20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2208.03657
openalex publication_date 2022/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce a new look at Finsler surfaces. Landsberg surfaces are Finsler surfaces that are solutions of a system of non-linear partial differential equations. Considering the unicorn's Landsberg problem, we reduce this system to a single non-linear PDE which we call the Landsberg's PDE. By making use of the new look of Finsler surfaces, we solve the Landsberg's PDE and get a class of solutions. Moreover, we show that these solutions and their conformal transformations are Berwaldain.