Gauge transformations of Jacobi structures and contact groupoids

TL;DR

This paper introduces gauge transformations for Jacobi structures, explores their relation to Poisson structures through Poissonization, and examines how these transformations affect the contact structures of contact groupoids.

Contribution

It defines gauge transformations for Jacobi structures and analyzes their impact on contact groupoids, connecting Jacobi and Poisson geometries.

Findings

Gauge transformations of Jacobi structures are formally defined.

The relation between Jacobi and Poisson structures via Poissonization is clarified.

The effect of gauge transformations on contact groupoid structures is discussed.

Abstract

We define gauge transformations of Jacobi structures on a manifold. This is related to gauge transformations of Poisson structures via the Poissonization. Finally, we discuss how the contact structure of a contact groupoid is effected by a gauge transformation of the Jacobi structure on its base.