Geodesic
The contact system on the $(m, \ell )$-jet spaces
Archivum mathematicum, Tome 37 (2001) no. 4, pp. 291-300.

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This paper is a continuation of [MMR:98], where we give a construction of the canonical Pfaff system $\Omega (M_m^\ell )$ on the space of $(m,\ell )$-velocities of a smooth manifold $M$. Here we show that the characteristic system of $\Omega (M_m^\ell )$ agrees with the Lie algebra of $\operatorname{Aut}({\mathbb R}_m^\ell )$, the structure group of the principal fibre bundle ${\check{M}}_m^\ell \longrightarrow J_m^\ell (M)$, hence it is projectable to an irreducible contact system on the space of $(m,\ell )$-jets ($=\ell $-th order contact elements of dimension $m$) of $M$. Furthermore, we translate to the language of Weil bundles the structure form of jet fibre bundles defined by Goldschmidt and Sternberg in [Gol:Ste:73].
Classification : 58A17, 58A20
Keywords: near points; jets; contact elements; contact system; velocities 
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     title = {The contact system on the $(m, \ell )$-jet spaces},
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Muñoz, J.; Muriel, F. J.; Rodríguez, J. The contact system on the $(m, \ell )$-jet spaces. Archivum mathematicum, Tome 37 (2001) no. 4, pp. 291-300. http://geodesic.mathdoc.fr/item/ARM_2001__37_4_a5/