The Local Structure of Generalized Contact Bundles
@article{Schnitzer2017TheLS, title={The Local Structure of Generalized Contact Bundles}, author={Jonas Schnitzer and Luca Vitagliano}, journal={International Mathematics Research Notices}, year={2017} }
Generalized contact bundles are odd-dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local splitting theorem similar to those appearing in Poisson geometry. In particular, in a neighborhood of a regular point, a generalized contact bundle is either the product of a contact and a complex manifold or the product of a symplectic manifold and a…
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45 References
Local structure of generalized complex manifolds
- Mathematics
- 2004
We 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…
Local classification of generalized complex structures
- Mathematics
- 2012
We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson…
Generalized contact structures
- MathematicsJ. Lond. Math. Soc.
- 2011
Using a Boothby-Wang construction bridging symplectic structures and contact structures, examples are found to demonstrate that, within the category of generalized contacts, classical contact structures have non-trivial deformations.
Splitting theorems for Poisson and related structures
- MathematicsJournal für die reine und angewandte Mathematik (Crelles Journal)
- 2019
Abstract According to the Weinstein splitting theorem, any Poisson manifold is locally, near any given point, a product of a symplectic manifold with another Poisson manifold whose Poisson structure…
Generalized Complex Geometry
- MathematicsUniversity Lecture Series
- 2004
Generalized complex geometry encompasses complex and symplectic ge- ometry as its extremal special cases. We explore the basic properties of this geometry, including its enhanced symmetry group,…
Holomorphic Jacobi Manifolds and Complex Contact Groupoids
- Mathematics
- 2017
This is the second part of a series of two papers dedicated to a systematic study of holomorphic Jacobi structures. In the first part, we introduced and study the concept of a holomorphic Jacobi…
Generalized almost contact structures and generalized Sasakian structures
- Mathematics
- 2012
We introduce generalized almost contact structures which admit the $B$-field transformations on odd dimensional manifolds. We provide definition of generalized Sasakain structures from the view point…