MMN-4390
A new look at Finsler surfaces and Landsberg's PDE
Salah G. Elgendi;Abstract
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 PDEvwhich 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 andvtheir conformal transformations are Berwaldain
Vol. 25 (2024), No. 1, pp. 209-223