Godbillon-Vey classes of regular Jacobi manifolds

TL;DR

This paper explores the Godbillon-Vey class in regular Jacobi manifolds, providing explicit expressions in terms of Jacobi structures, thereby extending geometric characteristic class theory.

Contribution

It introduces an explicit formula for the Godbillon-Vey class in regular Jacobi manifolds, generalizing characteristic classes to this setting.

Findings

Derived explicit expressions for the Godbillon-Vey class in Jacobi manifolds.

Connected the class to the underlying Jacobi structures and foliations.

Extended the understanding of characteristic classes in contact and conformal symplectic geometries.

Abstract

The notion of a Jacobi manifold is a natural generalization of that of a Poisson manifold. A Jacobi manifold has a natural foliation in which each leaf has either a contact structure or a locally conformal symplectic structure. In this paper, we study a characteristic class called the Godbillon-Vey class for Jacobi manifolds with regular foliation and express it explicitly in terms of Jacobi structures.