Differential Geometry
Dirac structures and paracomplex manifolds
Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 889-894.

We introduce the notion of a generalized paracomplex structure. This is a natural notion which unifies several geometric structures such as symplectic forms, paracomplex structures, and Poisson structures. We show that generalized paracomplex structures are in one-to-one correspondence with pairs of transversal Dirac structures on a smooth manifold.

Nous introduisons la notion de structure paracomplexe généralisée. Il s'agit d'une notion naturelle qui unifie plusieurs structures géométriques telles que les formes symplectiques, les structures paracomplexes et les structures de Poisson. Nous montrons que, sur une variété différentiable, les structures paracomplexes généralisées sont en correspondance biunivoque avec les couples de structures de Dirac transverses.

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DOI: 10.1016/j.crma.2004.03.031
Wade, Aïssa 1

1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
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Wade, Aïssa. Dirac structures and paracomplex manifolds. Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 889-894. doi : 10.1016/j.crma.2004.03.031. http://www.numdam.org/articles/10.1016/j.crma.2004.03.031/

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