Affine structure on Weil bundles. (English) Zbl 0961.58002

Kolář, Ivan

Nagoya Math. J. 158, 99-106 (2000).

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

Keywords:

Weil bundle; affine bundle; contact elements