A variational problem for curves on Riemann-Finsler surfaces
  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. 
Sorin V. Sabau and Kazuhiro Shibuya
math.DG