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The contact system on the ( m , ) -jet spaces

J. MuñozF. J. MurielJosemar Rodríguez — 2001

Archivum Mathematicum

This paper is a continuation of [MMR:98], where we give a construction of the canonical Pfaff system Ω ( M m ) on the space of ( m , ) -velocities of a smooth manifold M . Here we show that the characteristic system of Ω ( M m ) agrees with the Lie algebra of Aut ( m ) , the structure group of the principal fibre bundle M ˇ m J m ( M ) , hence it is projectable to an irreducible contact system on the space of ( m , ) -jets ( = -th order contact elements of dimension m ) of M . Furthermore, we translate to the language of Weil bundles the structure form...

The contact system for A -jet manifolds

R. J. Alonso-BlancoJ. Muñoz-Díaz — 2004

Archivum Mathematicum

Jets of a manifold M can be described as ideals of 𝒞 ( 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 derived algebra.

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