Locally Lagrangian Symplectic and Poisson Manifolds

TL;DR

This paper explores locally Lagrangian symplectic and Poisson manifolds, detailing their properties, examples, and the computation of Maslov classes, and extends the concepts to Poisson structures.

Contribution

It introduces the concept of locally Lagrangian structures on symplectic and Poisson manifolds, providing examples, properties, and generalizations.

Findings

Characterization of locally Lagrangian symplectic manifolds

Computation methods for Maslov classes of Lagrangian submanifolds

Extension of structures to Poisson manifolds

Abstract

We discuss symplectic manifolds where, locally, the structure is that encountered in Lagrangian dynamics. Exemples 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 structures to Poisson manifolds.