The contact system on the $(m, \ell )$-jet spaces
Muñoz, J. ; Muriel, F. J. ; Rodríguez, Josemar
Archivum Mathematicum, Tome 037 (2001), p. 291-300 / Harvested from Czech Digital Mathematics Library
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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].

Publié le : 2001-01-01
Classification:  58A17,  58A20 
@article{107807,
     author = {J. Mu\~noz and F. J. Muriel and Josemar Rodr\'\i guez},
     title = {The contact system on the $(m, \ell )$-jet spaces},
     journal = {Archivum Mathematicum},
     volume = {037},
     year = {2001},
     pages = {291-300},
     zbl = {1090.58006},
     mrnumber = {1879452},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107807}
}

Muñoz, J.; Muriel, F. J.; Rodríguez, Josemar. The contact system on the $(m, \ell )$-jet spaces. Archivum Mathematicum, Tome 037 (2001) pp. 291-300. http://gdmltest.u-ga.fr/item/107807/

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