Hamiltonian vector fields on Weil bundles

TL;DR

This paper characterizes Hamiltonian vector fields on Weil bundles derived from Poisson and symplectic manifolds, extending classical concepts to these geometric structures.

Contribution

It provides a new characterization of Hamiltonian fields on Weil bundles associated with Poisson and symplectic manifolds, enriching the geometric theory.

Findings

Hamiltonian vector fields are characterized on Weil bundles.

The work extends classical Hamiltonian theory to Weil bundle context.

Provides foundational results for geometric structures on Weil bundles.

Abstract

Let M be a paracompact smooth manifold, A a Weil algebra and M^{A} the associated Weil bundle. In this paper, we give a characterization of hamiltonian field on M^{A} in the case of Poisson manifold and of Symplectic manifold.