Generalized contact structures

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 odddimensional 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 threedimensional Heisenberg group and its co-compact quotients. Address: Department of Mathematics, University of California at Riverside, Riverside CA 92521, U.S.A., Email: [email protected]. Partially supported by UCMEXUS and NSF-0906264 Address: Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, U.S.A., Email: [email protected]