Contact Dual Pairs

Abstract

We introduce and study the notion of contact dual pair adopting a line bundle approach to contact and Jacobi geometry. A contact dual pair is a pair of Jacobi morphisms defined on the same contact manifold and satisfying a certain orthogonality condition. Contact groupoids and contact reduction are the main sources of examples. Among other properties, we prove the Characteristic Leaf Correspondence Theorem for contact dual pairs which parallels the analogous result of Weinstein for symplectic dual pairs.

v2: 36 pages, minor revisions, final version to appear in IMRN, comments still welcome!

References in corpus (6)

• On local integration of Lie brackets
• Holomorphic Jacobi Manifolds and Holomorphic Contact Groupoids
• Differential forms with values in VB-groupoids
• The Local Structure of Generalized Contact Bundles
• Deformations of coisotropic submanifolds in Jacobi manifolds
• Normal Forms for Dirac-Jacobi bundles and Splitting Theorems for Jacobi Structures

Cited by in corpus (3)

• Multiplicative Connections and Their Lie Theory
• Contact line bundles, foliations, and integrability
• The Deformation $L_{\infty }$ algebra of a Dirac--Jacobi structure