  This text proposes geometrical descriptions of all variational problems
invariant by conformal transformations in two variables. First a
characterisation in terms of C-Finsler manifolds, a suitable generalization of
Finsler manifolds, is given. Second Hamiltonian formalisms are explored, with
an emphasis on Caratheodory's formalism. Some of these considerations were
subsequently developped in papers with Joseph Kouneiher in math-ph/0004020 and
math-ph/0010036
