Résumé : I will present some results about the momentum polytopes of the multiplicity-free Hamiltonian compact manifolds acted on by a compact group which are Kählerizable. I shall give a characterization of these polytopes, explain how much they determine these manifolds and sketch some applications of this characterization - most of these results have been obtained jointly with G. Pezzini and B. Van Steirteghem.

Keywords : momentum polytopes; spherical varieties; compact and connected Hamiltonian manifold