Geodesic
Natural operators in the view of Cartan geometries
Archivum mathematicum, Tome 39 (2003) no. 1, pp. 57-75

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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.
Classification : 53A55, 58A20, 58A32
Keywords: Cartan geometry; gauge natural bundle; natural operator; natural sheaf; reductive Cartan geometry 
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     author = {Pan\'ak, Martin},
     title = {Natural operators in the view of {Cartan} geometries},
     journal = {Archivum mathematicum},
     pages = {57--75},
     publisher = {mathdoc},
     volume = {39},
     number = {1},
     year = {2003},
     mrnumber = {1982212},
     zbl = {1112.58301},
     language = {en},
     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/