Modesto Salgado

Hamiltonian systems on k-cosymplectic manifolds

The Hamiltonian framework on symplectic and cosymplectic manifolds is extended in order to consider classical field theories. To do this, the notion of k-cosymplectic manifold is introduced, and a suitable Hamiltonian formalism is developed so that the field equations for scalar and vector Hamiltonian functions are derived.

The Günther’s formalism in classical field theory: momentum map and reduction

The polysymplectic formalism in local field theory, developed by Gunther [J. Diff. Geom. 25, 23 (1987)], is revised. A new approach and new results on momentum maps and reduction are given.

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.

p-Almost tangent structures

In this paper, we introduce a new type of geometric structures (calledp-almost tangent structures). They are a natural generalization of almost tangent structures. Moreover, the tangent budle ofp1-velocitiesTp1M of any manifoldM carries a canonicalp-almost tangent structure (hence the name). We interpret ap-almost tangent structure as a type ofG-structure and stablish its integrability in terms of the vanishing of some tensor fields associated with it. Finally, the existence of an adapted symmetric connection is proved.

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

Gunther's formalism (k-symplectic formalism) in classical field theory: Skinner-Rusk approach and the evolution operator

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

-cosymplectic and the

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

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Reduction of polysymplectic manifolds

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

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

k