2011 | OriginalPaper | Buchkapitel
Submanifolds in Poisson geometry: a survey
verfasst von : Marco Zambon
Erschienen in: Complex and Differential Geometry
Verlag: Springer Berlin Heidelberg
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We describe various classes of submanifolds of a Poisson manifold
M
, both in terms of tensors on
M
and of constraints: coisotropic submanifolds, Poisson- Dirac submanifolds (which inherit a Poisson structure), and the very general class of pre-Poisson submanifolds. We discuss embedding results for these classes of submanifolds, quotient Poisson algebras associated to them, and their relationship to subgroupoids of the symplectic groupoid of
M
.