65 citations · 261 across the 23 of their papers we have counts for
5 papers · 1 filter
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…
On Darboux theorems for geometric structures induced by closed forms
Xavier Gràcia, Javier de Lucas, Xavier Rivas +1
This work reviews the classical Darboux theorem for symplectic, presymplectic, and cosymplectic manifolds (which are used to describe regular and singular mechanical systems), and…
On k-polycosymplectic Marsden-Weinstein reductions
J. de Lucas, X. Rivas, S. Vilariño +1
We review and slightly improve the known k-polysymplectic Marsden--Weinstein reduction theory by removing some technical conditions on k-polysymplectic momentum maps by developing…