# Contact Dual Pairs

## TL;DR

This paper introduces contact dual pairs in Jacobi geometry, establishing their properties and examples, including a key leaf correspondence theorem analogous to Weinstein's symplectic case.

## Contribution

It defines contact dual pairs using a line bundle approach and proves a characteristic leaf correspondence theorem, advancing contact and Jacobi geometry understanding.

## Key findings

- Contact dual pairs are pairs of Jacobi morphisms with an orthogonality condition.
- The paper proves a characteristic leaf correspondence theorem for contact dual pairs.
- Examples include contact groupoids and contact reduction.

## 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.