E-mail: naca@math.muni.cz
Abstract.
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.
AMSclassification. 58A20, 53A55.
Keywords. Cartan geometry, gauge natural bundle, natural operator, natural sheaf, reductive Cartan geometry.