A review on coisotropic reduction in Symplectic, Cosymplectic, Contact and Co-contact Hamiltonian systems

TL;DR

This paper reviews the process of coisotropic reduction across various geometric structures in Hamiltonian systems, highlighting its role in simplifying dynamics by focusing on Lagrangian or Legendrian submanifolds.

Contribution

It provides a comprehensive overview of coisotropic reduction in symplectic, cosymplectic, contact, and co-contact Hamiltonian systems, emphasizing its geometric and dynamical significance.

Findings

Coisotropic reduction links dynamics to Lagrangian and Legendrian submanifolds.

Reduction techniques are applicable across multiple geometric frameworks.

The paper clarifies the role of coisotropic submanifolds in simplifying Hamiltonian systems.

Abstract

In this paper we study the coisotropic reduction in different types of dynamics according to the geometry of the corresponding phase space. The relevance of the coisotropic reduction is motivated by the fact that these dynamics can always be interpreted as Lagrangian or Legendrian submanifolds. Furthermore, Lagrangian or Legendrian submanifolds can be reduced by a coisotropic one.