The contact system for $A$-jet manifolds

R. J. Alonso-Blanco and J. Munoz-Diaz

 Departamento de Matematicas, Universidad de Salamanca, Plaza de la Merced 1-4, E-37008 Salamanca, Spain


Jets of a manifold $M$ can be described as ideals of $\C^\infty(M)$. This way, all the usual processes on jets can be directly referred to that ring. By using this fact, we give a very simple construction of the contact system on jet spaces. The same way, we also define the contact system for the recently considered $A$-jet spaces, where $A$ is a Weil algebra. We will need to introduce the concept of \emph{derived algebra}.

AMSclassification. 58A20.

Keywords.  Jet, contact system, Weil algebra, Weil bundle.