In this paper a Weil approach to quasijets is discussed. For given manifolds $M$ and $N$, a quasijet with source $x\in M$ and target $y\in N$ is a mapping $T_x^{r}M\to T_y^{r}N$ which is a vector homomorphism for each one of the $r$ vector bundle structures of the iterated tangent bundle $T^r$ [A. Dekrét, Casopis Pest. Mat. 111, No. 4, 345-352 (1986; Zbl 0611.58004)]. Let us denote by $Q{J}^r(M,N)$ the bundle of quasijets from $M$ to $N$; the space ${\tilde{J}}^r(M,N)$ of non-holonomic $r$-jets from $M$ to $N$ is embeded into $Q{J}^r(M,N)$. On the other hand, the bundle $Q{T}_m^{r}N$ of $(m,r)$-quasivelocities of $N$ is defined to be $Q{J}_0^r({𝐑}^m,N)$; then, $Q{T}_m^r$ is a product preserving functor and so a Weil functor $T^{{𝐐}_m^r}$ where ${𝐐}_m^r$ is the Weil algebra $Q{T}_m^r𝐑$ [see I. Kolár, P. Michor and J. Slovák, ‘Natural operations in differential geometry’ (Springer-Verlag, Berlin) (1993; Zbl 0782.53013)]; next, t!

EUDML-ID : urn:eudml:doc:220810
Mots clés:

@article{701662,
     title = {On quasijet bundles},
     booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {2000},
     pages = {187-196},
     mrnumber = {MR1764094},
     zbl = {0971.58003},
     url = {http://dml.mathdoc.fr/item/701662}
}

Tomáš, Jiří. On quasijet bundles, dans Proceedings of the 19th Winter School "Geometry and Physics", GDML_Books,  (2000), pp. 187-196. http://gdmltest.u-ga.fr/item/701662/