Marsden--Meyer--Weinstein reduction for k-contact field theories

2025/05/08 by J. de Lucas, X. Rivas, de Lucas, J. +5 · 2 citations
Engineering · Materials Science · Mathematics · #53C10 (Secondary) #53C12 #53C15 #53C30 (Primary) #53D05 #53D10 #Composite Material Mechanics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microstructure and mechanical properties #Nonlinear Partial Differential Equations #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2505.05462

openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work devises a Marsden--Meyer--Weinstein k-contact reduction. Our techniques are illustrated with several examples of mathematical and physical relevance. As a byproduct, we review the previous contact reduction literature so as to clarify and to solve some inaccuracies.

Citations

• Generalised subbundles and distributions: A comprehensive review
• On Darboux theorems for geometric structures induced by closed forms
• Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws
• Geometrical aspects of contact mechanical systems and field theories
• Contact geometry for simple thermodynamical systems with friction
• Multisymplectic structures and invariant tensors for Lie systems
• Methods of Differential Geometry in Classical Field Theories: k-symplectic and k-cosymplectic approaches
• Lagrangian submanifolds in k-symplectic settings
• Contact Reduction
• The Topological Structure of Contact and Symplectic Quotients

Cited by

• Reduction of exact symplectic manifolds and energy hypersurfaces
• Multisymplectic observable reduction using constraint triples

Related

• Contact Reduction
• Some contributions to k-contact Lagrangian field equations, symmetries and dissipation laws
• Contact reductions, mechanics and duality
• Tight and overtwisted contact structures
• Foundations on k-contact geometry