Non-holonomic \((r,s,q)\)-jets. (English) Zbl 1164.58304

Tomáš, Jiří M.

Czech. Math. J. 56, No. 4, 1131-1145 (2006).

Summary: 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 \(\tilde {J}^{r,s,q}_1\: 2\)-\(\mathcal F \mathcal M _{k,l} \to \mathcal F \mathcal M\) defined on the category of \(2\)-fibered manifolds with \(\mathcal F \mathcal M _{k,l}\)-underlying objects.

MSC:

58A05	Differentiable manifolds, foundations
58A20	Jets in global analysis

Keywords:

bundle functor; jet; non-holonomic jet; Weil bundle

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