Geodesic
Non-holonomic $(r,s,q)$-jets
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 4, pp. 1131-1145 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We generalize the concept of an $(r,s,q)$-jet to the concept of a non-holonomic $(r,s,q)$-jet. We define the composition of such objects and introduce a bundle functor ${\tilde{J}}^{r,s,q}\: \mathcal{F}\mathcal{M}_{k,l} \times \mathcal{F}\mathcal{M}$ defined on the product category of $(k,l)$-dimensional fibered manifolds with local fibered isomorphisms and the category of fibered manifolds with fibered maps. We give the description of such functors from the point of view of the theory of Weil functors. Further, we introduce a bundle functor $\tilde{J}^{r,s,q}_1\: 2\text{-}\mathcal{F}\mathcal{M}_{k,l} \rightarrow \mathcal{F}\mathcal{M}$ defined on the category of $2$-fibered manifolds with $\mathcal{F}\mathcal{M}_{k,l}$-underlying objects.
We generalize the concept of an $(r,s,q)$-jet to the concept of a non-holonomic $(r,s,q)$-jet. We define the composition of such objects and introduce a bundle functor ${\tilde{J}}^{r,s,q}\: \mathcal{F}\mathcal{M}_{k,l} \times \mathcal{F}\mathcal{M}$ defined on the product category of $(k,l)$-dimensional fibered manifolds with local fibered isomorphisms and the category of fibered manifolds with fibered maps. We give the description of such functors from the point of view of the theory of Weil functors. Further, we introduce a bundle functor $\tilde{J}^{r,s,q}_1\: 2\text{-}\mathcal{F}\mathcal{M}_{k,l} \rightarrow \mathcal{F}\mathcal{M}$ defined on the category of $2$-fibered manifolds with $\mathcal{F}\mathcal{M}_{k,l}$-underlying objects.
Classification : 58A05, 58A20, 58A32
Keywords: bundle functor; jet; non-holonomic jet; Weil bundle 
@article{CMJ_2006_56_4_a4,
     author = {Tom\'a\v{s}, Ji\v{r}{\'\i} M.},
     title = {Non-holonomic $(r,s,q)$-jets},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1131--1145},
     year = {2006},
     volume = {56},
     number = {4},
     mrnumber = {2280799},
     zbl = {1164.58304},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_4_a4/}
}
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Tomáš, Jiří M. Non-holonomic $(r,s,q)$-jets. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 4, pp. 1131-1145. http://geodesic.mathdoc.fr/item/CMJ_2006_56_4_a4/