Jets and contact elements. (English) Zbl 1020.58002

Krupka, D. (ed.), Proceedings of the seminar on differential geometry, Opava, Czech Republic, 2000. Opava: Silesian University at Opava. Math. Publ. (Opava). 2, 39-85 (2000).
The article offers a very thorough treatment of jets of higher orders and higher order jet prolongations of a lot of objects. It starts from the very beginning, defining the jets of smooth mappings, composition of jets, higher order frames, velocities,…. It follows the description of the following manifolds of jets: higher order differential groups, Grassmann prolongations of manifolds, jet prolongations of fibered manifolds, jet prolongations of Lie groups, principal and associated bundles.
It contains a lot of explicit formulas, as of the group structure on jet groups, actions of the jet groups on the above mentioned manifolds of jets.
There are a few very technical results in the article. It can serve as a survey of basic constructions including jets.
For the entire collection see [Zbl 0980.00034].


58A20 Jets in global analysis