Generalized Contact Bundles

Abstract

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.

Short Note: 8 pages. Minor revisions. Published in C. R. Math. Comments welcome!

References in corpus (2)

• Poisson Quasi-Nijenhuis Manifolds
• Remarks on Contact and Jacobi Geometry

Cited by in corpus (15)

• Remarks on Contact and Jacobi Geometry
• Holomorphic Jacobi Manifolds and Holomorphic Contact Groupoids
• Infinitesimal Automorphisms of VB-groupoids and algebroids
• Jacobi bundles and the BFV-complex
• Jacobi sigma models
• The Local Structure of Generalized Contact Bundles
• Contact structures on Lie algebroids
• Topological and dynamical aspects of Jacobi sigma models
• Generalised contact geometry as reduced generalised complex geometry
• VB-Courant algebroids, E-Courant algebroids and generalized geometry
• Higher omni-Lie algebroids
• Gauge transformations of Jacobi structures and contact groupoids
• Jacobi Geometry and Hamiltonian Mechanics: the Unit-Free Approach
• Regular Jacobi Structures and Generalized Contact Bundles
• The Deformation $L_{\infty }$ algebra of a Dirac--Jacobi structure