60 citations · 91 across the 5 of their papers we have counts for
5 papers
Geometry of Riccati equations over normed division algebras
J. de Lucas, M. Tobolski, S. Vilariño
This work presents and studies Riccati equations over finite-dimensional normed division algebras. We prove that a Riccati equation over a finite-dimensional normed division algebr…
A new application of k-symplectic Lie systems
J. de Lucas, M. Tobolski, S. Vilariño
The -symplectic structures appear in the geometric study of the partial differential equations of classical field theories. Meanwhile, we present a new application of the -sy…
Methods of Differential Geometry in Classical Field Theories: k-symplectic and k-cosymplectic approaches
M. de León, M. Salgado, S. Vilariño
This book is devoted to review two of the most relevant approaches to the study of classical field theories of first order, say k-symplectic and k-cosymplectic. In the last part, w…
Hamilton-Jacobi theory in k-cosymplectic field theories
M. de León, S. Vilariño
In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for time dependent Mechanics to the case of classical field theories in the k-cosymplectic framework.
SOPDEs and Nonlinear Connections
N. Román-Roy, M. Salgado, S. Vilariño
The canonical k-tangent structure on allows us to characterize nonlinear connections on and to develop Günther's (k-symplectic) L…