Silvia Vilariño

Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory

This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noethers theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.

On the k-symplectic, k-cosymplectic and multisymplectic formalisms of classical field theories

The objective of this work is twofold: First, we analyze the relation between the

On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory

k

Methods of differential geometry in classical field theories : k-symplectic and k-cosymplectic approaches

-cosymplectic and the

Reduction of polysymplectic manifolds

k

k-Symplectic Lie systems: theory and applications

-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between

HAMILTON–JACOBI THEORY IN k-COSYMPLECTIC FIELD THEORIES

k

k-SYMPLECTIC AND k-COSYMPLECTIC LAGRANGIAN FIELD THEORIES: SOME INTERESTING EXAMPLES AND APPLICATIONS

-symplectic field theories and the so-called autonomous

k-SYMPLECTIC FORMALISM ON LIE ALGEBROIDS

k

k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner–Rusk Formulations

-cosymplectic field theories, extending in this way the description of the symplectic formalism of autonomous systems as a particular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between