nLab symplectic leaf

Idea

For $(X, \{-,-\})$ a Poisson manifold, a symplectic leaf is a maximal connected submanifold $Y \hookrightarrow X$ on which the Poisson bracket restricts to a symplectic manifold structure.

$X$ is foliated by its symplectic leaves.

References

Regular foliations by symplectic leafs have originally been found and studied in

• F. Bayen, M. Flato, C. Fronsdal, A. Lichnerovicz & D. Sternheimer, Deformation theory and quantization, Ann. Phys. I l l (1978) 61-151.

A detailed technical review is in the notes

• Jordan Watts, An introduction to Poisson manifolds (2007) (pdf)