Geometrie affine Geometrie symplectique

摘要

Let (M,w,L) be a symplectic manifold endowed with a lagrangian foliation L.Liberman and Weinstein have shown that the leaves of L are endowed with anaffine structure. In this paper we provide links between the theories of affinemanifolds and symplectic geometry. Using the work of Donaldson who have shownthe existence of symplectic submanifolds in every codimension, we show theAuslander conjecture to be true if the linear holonomy is contained in Gl(n,Z)