We prove the (first) reduction theorem for general and classical connections, i.e. we prove that any natural operator of a general connection Γ on a fibered manifold and a classical connection Λ on the base manifold can be expressed as a zero order operator of the curvature tensors of Γ and Λ and their appropriate derivatives.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-3-4,
author = {Josef Jany\v ska},
title = {Reduction theorem for general connections},
journal = {Annales Polonici Mathematici},
volume = {101},
year = {2011},
pages = {231-254},
zbl = {1239.53033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-3-4}
}
Josef Janyška. Reduction theorem for general connections. Annales Polonici Mathematici, Tome 101 (2011) pp. 231-254. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-3-4/