# Constraint algorithm for singular field theories in the $k$-cosymplectic framework

## TL;DR

This paper develops a constraint algorithm within the $k$-cosymplectic framework to handle singular classical field theories, introducing $k$-precosymplectic structures and applying it to affine Lagrangians.

## Contribution

It introduces $k$-precosymplectic structures and a constraint algorithm for singular field theories in the $k$-cosymplectic setting, extending the geometric framework.

## Key findings

- Established a $k$-precosymplectic structure for singular theories
- Developed a constraint algorithm to find solution submanifolds
- Applied the framework to affine Lagrangian examples

## Abstract

The aim of this paper is to develop a constraint algorithm for singular classical field theories in the framework of $k$-cosymplectic geometry. Since these field theories are singular, we need to introduce the notion of $k$-precosymplectic structure, which is a generalization of the $k$-cosymplectic structure. Next $k$-precosymplectic Hamiltonian systems are introduced in order to describe singular field theories, both in Lagrangian and Hamiltonian formalisms. Finally, we develop a constraint algorithm in order to find a submanifold where the existence of solutions of the field equations is ensured. The case of affine Lagrangians is studied as a relevant example.