Geodesic
Natural operators in the view of Cartan geometries
Archivum mathematicum, Tome 39 (2003) no. 1, pp. 57-75 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We prove, that $r$-th order gauge natural operators on the bundle of Cartan connections with a target in the gauge natural bundles of the order $(1,0)$ (“tensor bundles”) factorize through the curvature and its invariant derivatives up to order $r-1$. On the course to this result we also prove that the invariant derivations (a generalization of the covariant derivation for Cartan geometries) of the curvature function of a Cartan connection have the tensor character. A modification of the theorem is given for the reductive and torsion free geometries.
We prove, that $r$-th order gauge natural operators on the bundle of Cartan connections with a target in the gauge natural bundles of the order $(1,0)$ (“tensor bundles”) factorize through the curvature and its invariant derivatives up to order $r-1$. On the course to this result we also prove that the invariant derivations (a generalization of the covariant derivation for Cartan geometries) of the curvature function of a Cartan connection have the tensor character. A modification of the theorem is given for the reductive and torsion free geometries.
Classification : 53A55, 58A20, 58A32
Keywords: Cartan geometry; gauge natural bundle; natural operator; natural sheaf; reductive Cartan geometry 
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     url = {http://geodesic.mathdoc.fr/item/ARM_2003_39_1_a5/}
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Panák, Martin. Natural operators in the view of Cartan geometries. Archivum mathematicum, Tome 39 (2003) no. 1, pp. 57-75. http://geodesic.mathdoc.fr/item/ARM_2003_39_1_a5/

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