Hamiltonian structures on foliations

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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 socalled tame case, the structure is induced by a Poisson structure of the manifold. Cohomology spaces and classes relevant to geometric quantization are also considered.

Original languageEnglish
Pages (from-to)4966-4977
Number of pages12
JournalJournal of Mathematical Physics
Issue number10
StatePublished - 1 Oct 2002

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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