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A general point of view to nonholonomic jet bundles. (English) Zbl 1048.58002
In the present paper are some classification results concerning nonholonomic jet bundle functors and their geometrical interpretation obtained.
The starting point is the already published abstract result on jet bundle functors defined on the product category \(\mathcal M f_m \times \mathcal M f\) and on the category \(\mathcal F\mathcal M_m\) formulated in terms of the Weil theory, where the symbols denote the category of \(m\)-dimensional manifolds, the category of manifolds and the category of fibered manifolds with \(m\)-dimensional bases.
This result appears usefull for deducing interesting geometrical properties and classification results on nonholonomic jet bundles. It is proved that the only second order jet functors are nonholonomic jets \(\widetilde{J}^2\), semiholonomic jets \(\overline{J}^2\) and holonomic jets \(J^2\). Moreover, it is proved that the only third order jet bundle with the property that its three canonical projections to the first order are geometrically independent is the whole third order nonholonomic jet bundle. Finally, all jet subfunctors of the functor \(\overline{J}^{r,r-1}\) of semiholonomic \(r\)-th order jets are described.

MSC:
58A20 Jets in global analysis
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References:
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