Reduced classical field theories. k-cosymplectic formalism on Lie algebroids

TL;DR

This paper develops a geometric framework for classical field theories on Lie algebroids using k-cosymplectic geometry, generalizing standard theories and exploring reductions and transformations.

Contribution

It introduces a novel geometric formalism for Lagrangian and Hamiltonian theories on Lie algebroids within the k-cosymplectic setting, extending classical approaches.

Findings

Established a Legendre transformation between Lagrangian and Hamiltonian formalisms.

Generalized classical field theories to Lie algebroids.

Analyzed reduction processes in the context of the new formalism.

Abstract

In this paper we introduce a geometric description of Lagrangian and Hamiltonian classical field theories on Lie algebroids in the framework of $k$-cosymplectic geometry. We discuss the relation between Lagrangian and Hamiltonian descriptions through a convenient notion of Legendre transformation. The theory is a natural generalization of the standard one; in addition, other interesting examples are studied, mainly on reduction of classical field theories.