On the local structure of Dirac manifolds

Abstract

We give a local normal form for Dirac structures. As a consequence, we show that the dimensions of the pre-symplectic leaves of a Dirac manifold have the same parity. We also show that, given a point $m$ of a Dirac manifold $M$, there is a well-defined transverse Poisson structure to the pre-symplectic leaf $P$ through $m$. Finally, we describe the neighborhood of a pre-symplectic leaf in terms of geometric data. This description agrees with that given by Vorobjev for the Poisson case

minor corrections

Cited by in corpus (7)

• Tensor products of Dirac structures and interconnection in Lagrangian mechanical systems
• Dirac structures and Nijenhuis operators
• The Local Structure of Generalized Contact Bundles
• Integration of Coupling Dirac Structures
• Removable presymplectic singularities and the local splitting of Dirac structures
• Complex Dirac structures: invariants and local structure
• The Hamiltonian formalism of the Inverse Problem