ON LAGRANGIAN FOLIATIONS WITH LINEAR HOLONOMY

Let (M, F, OMEGA) be a symplectic manifold with a Lagrangian foliation F and F0 a compact leaf of F. Our proposal in this Note is to give a partial result on the following problem: supposing the holonomy of F0 linearizes what can be said about the symplectic equivalence with (T* (F0). F(lin), OMEGA(can). After recalling the case dim M = 2 we give an example, for dim M = 4, F0 = T2, where this equivalence is not verified.