21 research outputs found
Generalized Contact Bundles
In this Note, we propose a line bundle approach to odd-dimensional analogues
of generalized complex structures. This new approach has three main advantages:
(1) it encompasses all existing ones; (2) it elucidates the geometric meaning
of the integrability condition for generalized contact structures; (3) in light
of new results on multiplicative forms and Spencer operators, it allows a
simple interpretation of the defining equations of a generalized contact
structure in terms of Lie algebroids and Lie groupoids.Comment: Short Note: 8 pages. Minor revisions. Published in C. R. Math.
Comments welcome
Contact manifolds and generalized complex structures
We give simple characterizations of contact 1-forms in terms of Dirac
structures. We also relate normal almost contact structures to the theory of
Dirac structures.Comment: 12 pages, typos correcte
Integration of Dirac-Jacobi structures
We study precontact groupoids whose infinitesimal counterparts are
Dirac-Jacobi structures. These geometric objects generalize contact groupoids.
We also explain the relationship between precontact groupoids and homogeneous
presymplectic groupoids. Finally, we present some examples of precontact
groupoids.Comment: 10 pages. Brief changes in the introduction. References update