Forma normal de uma estrutura de Poisson

Abstract

The present work consists of an introduction to the Poisson manifold concept and the presentation of some of the main results regarding the normal form for this structure, based on the works of Jean-Paull Dufour and NguyenTien Zung and Rui Loja. Initially ,Poisson structures in a manifold and the relationship we have with a symplectic manifold were studied. Later, we discussed symplectic foliations and how a Poisson structure can be obtained by this foliation. Finally, the Levi decomposition for Poisson manifold ,whic his a type of normal form for Poisson manifold, was studied.