A Jacobi Coupling Construction on Associated Bundles

We extend the Sternberg--Weinstein coupling construction to the Jacobi geometry setting.

Starting from a Jacobi Hamiltonian $G$-space and a principal bundle equipped with a connection whose curvature satisfies some nondegeneracy condition, we show that the associated bundle naturally carries a Jacobi structure compatible with the canonical ones on the fibers.

This construction provides a unified framework encompassing the symplectic, locally conformal symplectic, and contact cases.

It reveals new coupling phenomena related to the presence of the Reeb vector field.