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

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.

MSC:

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