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Affine structure on Weil bundles. (English) Zbl 0961.58002

For every \(r\)th-order Weil functor \(T^A\), the author introduces the underlying \(k\)th-order Weil functors \(T^{A_k}\), \(k= 1,\dots, r-1\). He deduces that \(T^A M\to T^{A_{r-1}}M\) is an affine bundle for every manifold \(M\). Generalizing the classical concept of contact element by C. Ehresman, the author defines the bundle of contact elements of type \(A\) on \(M\) and describes some affine properties of this bundle.
Reviewer: I.Kolář (Brno)

MSC:

58A20 Jets in global analysis
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