Jet manifold associated to a Weil bundle. (English) Zbl 1049.58007

Alonso, Ricardo J.

Arch. Math., Brno 36, No. 3, 195-199 (2000).

Given a Weil algebra \(A\) and a smooth manifold \(M\), the author defines an \(A\)-jet on \(M\) as the kernel of a regular \(A\)-point on \(M\). He proves that the set \(J^AM\) of all \(A\)-jets on \(M\) has a canonical manifold structure and \(\operatorname {reg}M^A\to J^AM\) is a principal fiber bundle with structure group \(\operatorname {Aut}A\), where \(\operatorname {reg}M^A\) denotes the space of all regular \(A\)-points on \(M\).

Reviewer: Ivan Kolář (Brno)

MSC:

58A20

Jets in global analysis

Keywords:

jet; Weil bundle; Grassmann manifold