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.
@article{107854,
author = {Martin Pan\'ak},
title = {Natural operators in the view of Cartan geometries},
journal = {Archivum Mathematicum},
volume = {039},
year = {2003},
pages = {57-75},
zbl = {1112.58301},
mrnumber = {1982212},
language = {en},
url = {http://dml.mathdoc.fr/item/107854}
}
Panák, Martin. Natural operators in the view of Cartan geometries. Archivum Mathematicum, Tome 039 (2003) pp. 57-75. http://gdmltest.u-ga.fr/item/107854/
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