On the local structure of Dirac manifolds

Jean Paul Dufour, Aïssa Wade

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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.

Original languageEnglish (US)
Pages (from-to)774-786
Number of pages13
JournalCompositio Mathematica
Issue number3
Publication statusPublished - May 1 2008

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Dufour, Jean Paul ; Wade, Aïssa. / On the local structure of Dirac manifolds. In: Compositio Mathematica. 2008 ; Vol. 144, No. 3. pp. 774-786.