This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton–Jacobi theory. The relation with the “classical” Hamiltonian approach using canonical transformations ...

Consideramos en el espacio de parejas de tensores tension y deformacion la relacion de equivalencia que se corresponde con cambios de base ortonormales. Identificandolas con parejas de matrices cuadradas, podemos utilizar ...

Starting from the existence of a $C^{p}$-basis for any $C^{p}$-family of subspaces having constant dimension, we construct a Brunovsky basis of class $C^{p}$ for a $C^{p}$-family of pairs of matrices having constant ...

The geometric framework for the Hamilton-Jacobi theory developed in the studies of Carinena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Carinena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 ...

We consider a regular distribution D in a Riemannian manifold (M, g). The LeviCivita connection on (M, g) together with the orthogonal projection allow to endow the space of sections of D with a natural covariant derivative, ...

In previous papers, a geometric framework has been developed to describe non-conservative field theories as a kind of modified Lagrangian and Hamiltonian field theories. This approach is that of k-contact Hamiltonian ...

It studies the fundamental group of complex algebraic varieties, in its Betti, Hodge and de Rham realizations. This study has been carried out both in the absolute case, i.e. fundamental groups of such varieties, and in ...