Local structure of generalized complex manifolds

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dc.creatorAbouzaid, Mohammed
dc.creatorBoyarchenko, Mitya
dc.date2004-12-04
dc.date.accessioned2026-07-07T05:14:56Z
dc.date.available2026-07-07T05:14:56Z
dc.descriptionWe study generalized complex manifolds from the point of view of symplectic and Poisson geometry. We start by showing that every generalized complex manifold admits a canonical Poisson structure. We use this fact, together with Weinstein's classical result on the local normal form of Poisson manifolds, to prove a local structure theorem for generalized complex manifolds which extends the result Gualtieri has obtained in the "regular" case. Finally, we begin a study of the local structure of a generalized complex manifold in a neighborhood of a point where the associated Poisson tensor vanishes. In particular, we show that in such a neighborhood, a "first-order approximation" to the generalized complex structure is encoded in the data of a constant B-field and a complex Lie algebra.
dc.description18 pages, Latex
dc.identifierhttps://arxiv.org/abs/math/0412084
dc.identifierhttp://arxiv.org/abs/math/0412084
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73476
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.titleLocal structure of generalized complex manifolds
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