Generalized Contact Structures

TL;DR

This paper explores the integrability and deformation of generalized contact structures, introducing strong generalized contact structures, and constructs new examples and families on specific manifolds using Lie bialgebroid theory.

Contribution

It defines strong generalized contact structures, differentiates them from generalized complex structures, and constructs new examples and deformations on the Heisenberg group.

Findings

Classical contact structures can be non-trivially deformed within generalized contact structures.

New families of strong generalized contact structures are constructed on the Heisenberg group.

Conditions for integrability lead to the formation of Lie bialgebroids.

Abstract

We study integrability of generalized almost contact structures, and find conditions under which the main associated maximal isotropic vector bundles form Lie bialgebroids. These conditions differentiate the concept of generalized contact structures from a counterpart of generalized complex structures on odd-dimensional manifolds. We name the latter strong generalized contact structures. Using a Boothby-Wang construction bridging symplectic structures and contact structures, we find examples to demonstrate that, within the category of generalized contact structures, classical contact structures have non-trivial deformations. Using deformation theory of Lie bialgebroids, we construct new families of strong generalized contact structures on the three-dimensional Heisenberg group and its co-compact quotients.