Journal of Symplectic Geometry

Local structure of generalized complex manifolds

Mohammed Abouzaid and Mitya Boyarchenko

Full-text: Open access

Abstract

We study generalized complex (GC) manifolds from the point of view of symplectic and Poisson geometry. We start by recalling that every GC manifold admits a canonical Poisson structure. We use this fact, together with Weinstein's classical result on the local normal form of Poisson, to prove a local structure theorem for GC, complex manifolds, which extends the result Gualtieri has obtained in the "regular'' case. Finally, we begin a study of the local structure of a GC 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 GC structure is encoded in the data of a constant B-field and a complex Lie algebra.

Article information

Source
J. Symplectic Geom., Volume 4, Number 1 (2006), 43-62.

Dates
First available in Project Euclid: 2 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1154549057

Mathematical Reviews number (MathSciNet)
MR2240211

Zentralblatt MATH identifier
1116.53055

Citation

Abouzaid, Mohammed; Boyarchenko, Mitya. Local structure of generalized complex manifolds. J. Symplectic Geom. 4 (2006), no. 1, 43--62. https://projecteuclid.org/euclid.jsg/1154549057


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