The Local Structure of Generalized Contact Bundles

TL;DR

This paper investigates the local structure of generalized contact bundles, revealing a splitting theorem that characterizes their behavior near regular points as products of well-understood geometric structures.

Contribution

It establishes a local splitting theorem for generalized contact bundles, analogous to Poisson geometry, enhancing understanding of their local geometric structure.

Findings

Near regular points, generalized contact bundles split into products of contact and complex manifolds.

The local structure can also be described as products of symplectic manifolds and manifolds with integrable complex structures.

The results provide a foundational understanding of the local geometry of generalized contact bundles.

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.