A variational problem for curves on Riemann-Finsler surfaces

TL;DR

This paper investigates the variational problem for N-parallel curves on Finsler surfaces, deriving conditions for extremals of a length functional and explicitly formulating the Euler-Lagrange equations using Exterior Differential Systems.

Contribution

It introduces a novel approach to analyze N-parallel curves on Finsler surfaces via Exterior Differential Systems and provides explicit conditions and equations for extremals.

Findings

Derived conditions for N-parallel curves to be length functional extremals

Explicit Euler-Lagrange equations for the variational problem

Applied Griffiths' method to Finslerian surface curves

Abstract

We study the variational problem for $N$-parallel curves on a Finslerian surface by means of Exterior Differential Systems using Griffiths' method. We obtain the conditions when these curves are extremals of a length functional and write the explicit form of Euler-Lagrange equations for this type of variational problem.