On p-form vortex-lines equations on extended phase space

TL;DR

This paper generalizes vortex-line equations on extended phase space by replacing the differential 1-form with a differential p-form, exploring the resulting geometric structures and their implications in Hamiltonian systems.

Contribution

It introduces a new class of vortex-line equations using p-forms, extending the geometric framework of Hamiltonian dynamics.

Findings

Generalization of vortex-line equations to p-forms.

Analysis of the geometric structure of these equations.

Potential applications in advanced Hamiltonian systems.

Abstract

In differential-geometric language, vortex-lines equations on extended phase space of a system may be written as $i_{\dot \gamma}d\sigma =0$, where $\sigma$ is a differential 1-form. This is the structure, to give a paradigmatic example, of the Hamilton equations. Here, we study equations of the same structure, where $\sigma$ is a differential p-form.