Natural operators in the view of Cartan geometries. (English) Zbl 1112.58301

Panák, Martin

Arch. Math., Brno 39, No. 1, 57-75 (2003).

The author deduces that the \(r\)-th order natural operators on the bundle of Cartan connections with values in a gauge natural bundle of the order \((1,0)\) factorize through curvature and its invariants derivatives up to order \(r-1\). He also proves that the invariant derivations of the curvature function of a Cartan connection are of tensor character. A modification of this theorem is given for the reductive and torsion free geometries.

Reviewer: Ivan Kolář (Brno)

MSC:

58A20	Jets in global analysis
53A55	Differential invariants (local theory), geometric objects

Keywords:

gauge natural bundle; natural operator; natural sheaf; reductive Cartan geometry