Hamiltonian structures on foliations

Abstract

We discuss hamiltonian structures of the Gelfand-Dorfman complex of projectable vector fields and differential forms on a foliated manifold. Such a structure defines a Poisson structure on the algebra of foliated functions, and embeds the given foliation into a larger, generalized foliation with presymplectic leaves. In a so-called tame case, the structure is induced by a Poisson structure of the manifold. Cohomology spaces and classes relevant to geometric quantization are also considered.

LaTex, 18 pages

Cited by in corpus (4)

• Coupling Poisson and Jacobi structures on foliated manifolds
• Poisson structures on almost complex Lie algebroids
• The geometry of Lie algebroids and its applications to optimal control
• Higher order transverse bundles and riemannian foliations