Jacobi Structures in $\mathbb{R}^3$

F. Haas

Published 2005-05-20, updated 2005-08-03Version 2

The most general Jacobi brackets in $\mathbb{R}^3$ are constructed after solving the equations imposed by the Jacobi identity. Two classes of Jacobi brackets were identified, according to the rank of the Jacobi structures. The associated Hamiltonian vector fields are also constructed.