%0 Journal Article %T On Curvatures of Sections of Tensor Bundles %A P. I. Katsylo %J Mathematics %D 2003 %I arXiv %X We consider natural differential operations acting on sections of tensor vector bundles. Arrising problems can be reformulated as invariant theoretical problems (the IT-reduction). We give examples of usage of the IT-reduction. In particular, on a manifold with a connection and a Poisson structure we construct the canonical quantization. %U http://arxiv.org/abs/math/0306202v2