Mathematics – Symplectic Geometry
Scientific paper
2004-05-13
Mathematics
Symplectic Geometry
minor corrections
Scientific paper
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
Dufour Jean Paul
Wade Aïssa
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