The Local Structure of Generalized Contact Bundles
arXiv:1711.08310 · doi:10.1093/imrn/rnz009
Abstract
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 manifold equipped with an integrable complex structure on the gauge algebroid of the trivial line bundle.
v1: 38 pages, comments welcome! v2: 40 pages, minor revisions, added some remarks on almost contact structures in the appendix, final version to appear on IMRN