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/