65 citations · 261 across the 23 of their papers we have counts for
26 papers
From 2-covariant tensor fields to Poisson and Jacobi structures
Manuel de León, Xavier Gràcia, Rubén Izquierdo-López +2
Poisson and Jacobi structures play a fundamental role in the geometric description of many systems arising in classical mechanics. In most cases, the corresponding bivector field i…
Pairs of differential forms: a framework for precontact geometry
Xavier Gràcia, Àngel Martínez-Muñoz, Xavier Rivas
Precontact manifolds extend contact geometry by weakening the maximal non-integrability condition of the defining -form. We clarify the geometric foundations of this structure b…
Time-dependent metrics and connections
Xavier Gràcia, Xavier Rivas, Daniel Torres
Time-dependent structures often appear in differential geometry, particularly in the study of non-autonomous differential equations on manifolds. One may study the geodesics associ…
The evolution operator connecting the Lagrangian and Hamiltonian formalisms for contact systems
Xavier Gràcia, Ángel Martínez-Muñoz, Xavier Rivas +1
Some mechanical systems with dissipation can be described within the framework of the so-called contact mechanics: a modified form of the Euler-Lagrange equations stemming from Her…
Skinner--Rusk formalism of action-dependent multicontact field theories
Xavier Rivas, Narciso Román-Roy, Annamaria Villanova
The newly developed multicontact structure, based on contact and multisymplectic geometries, provides a very general geometrical framework suitable for the treatment of action-depe…
A survey on geometric frameworks for action-dependent classical field theories and their relationship
Jordi Gaset-Rifà, Xavier Rivas, Narciso Román-Roy
This work presents a comprehensive overview of three recently developed geometric frameworks for the study of classical action-dependent field theories. Specifically, the three und…