Abstract
We introduce the notion of a Jacobi bundle, which generalizes that of a Jacobi manifold. The construction of a Jacobi bundle over a conformal Jacobi manifold has, as particular cases, the constructions made by A. Weinstein [21] of a Le Brun-Poisson manifold over a contact manifold, and that of a Heisenberg-Poisson manifold over a symplectic (or Poisson) manifold. We show that the total space of a Jacobi bundle has a natural homogeneous Poisson structure, and that with each section of that bundle is associated a Hamiltonian vector field, defined on the total space of the bundle, tangent to the zero section, which projects onto the base manifold.
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