Liouville forms in a neighborhood of an isotropic embedding Frank Loose — 1997 Annales de l'institut Fourier A Liouville form on a symplectic manifold ( X , ω ) is by definition a potential β of the symplectic form - d β = ω . Its center M is given by β - 1 ( 0 ) . A normal form for certain Liouville forms in a neighborhood of its center is given.