We discuss symplectic manifolds where, locally, the structure is that encountered in Lagrangian dynamics. Examples and characteristic properties are given. Then, we refer to the computation of the Maslov classes of a Lagrangian submanifold. Finally, we indicate the generalization of this type of symplectic structures to Poisson manifolds. The paper is the text of a lecture presented at the Conference "Poisson 2000" held at CIRM, Luminy, France, between June 26 and June 30, 2000. It reviews results contained in the author's papers [9, 12, 13] as well as in papers by other authors.
|Number of pages||16|
|Journal||Rendiconti del Seminario Matematico|
|State||Published - 2001|
ASJC Scopus subject areas
- Mathematics (all)