k-cosymplectic classical field theories: Tulczyjew, Skinner--Rusk and Lie-algebroid formulations

Abstract

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations in terms of certain submanifolds of the tangent bundle of the $k^1$-velocities of a manifold. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics. Finally, both formalisms are formulated in terms of Lie algebroids.

This is a complete revised version of the former article: "k-cosymplectic formalism in classical field theory: the Skinner--Rusk approach". The paper has been enlarged, adding two new formulations of the k-cosymplectic formalism of field theories. The bibliography has been uploaded and completed. The title has been changed. 49 pp

References in corpus (8)

• Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories
• On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories
• Geometric Structures in Field Theory
• Discrete Lagrangian field theories on Lie groupoids
• Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory
• Unified formalism for non-autonomous mechanical systems
• Classical Field theory on Lie algebroids: multisymplectic formalism
• On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory

Cited by in corpus (7)

• A survey on cosymplectic geometry
• A new multisymplectic unified formalism for second-order classical field theories
• Classical field theories of first order and lagrangian submanifolds of premultisymplectic manifolds
• On Locally Conformally Cosymplectic Hamiltonian Dynamics and Hamilton-Jacobi Theory
• Properties of Multisymplectic Manifolds
• Skinner-Rusk formalism for k-contact systems
• Tulczyjew's derivations and intrinsic field equations in classical field theories