A new look at Finsler surfaces and Landsberg’s PDE

Elgendi, Salah G. (2024) A new look at Finsler surfaces and Landsberg’s PDE. Miskolc Mathematical Notes, 25 (1). pp. 209-223. ISSN 1787-2413

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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 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.

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