Problemes variationnels invariants par transformation conforme en dimension 2

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