Coisotropic embeddings of precosymplectic manifolds

TL;DR

This paper characterizes how precosymplectic manifolds can be embedded into cosymplectic manifolds, extending key symplectic geometry results to the time-dependent setting relevant for Hamiltonian mechanics.

Contribution

It provides a complete characterization of coisotropic embeddings in cosymplectic manifolds, extending Gotay's theorem and Weinstein's Darboux theorem to the cosymplectic case.

Findings

Extended Gotay's theorem to cosymplectic manifolds.

Generalized Weinstein's Darboux theorem for cosymplectic geometry.

Facilitates analysis of time-dependent Hamiltonian systems.

Abstract

In this paper we provide a complete characterisation of coisotropic embeddings of precosymplectic manifolds into cosymplectic manifolds. This result extends a theorem of Gotay about coisotropic embeddings of presymplectic manifolds. We also extend to the cosymplectic case some results of A. Weinstein which generalise the Darboux theorem. While symplectic geometry is the natural framework for developing Hamiltonian mechanics, cosymplectic geometry is the corresponding framework for time-dependent Hamiltonian mechanics. The motivation behind proving this theorem is to generalise known results for symplectic geometry to cosymplectic geometry, so that they can be used to study time-dependent systems, for instance for the regularization problem of singular Lagrangian systems.