On naturality of some construction of connections

Jan Kurek, Włodzimierz Mikulski


Let \(F\) be a bundle functor on the category of all fibred manifolds and fibred maps. Let \(\Gamma\) be a general connection in a fibred manifold \(\mathrm{pr}:Y\to M\) and \(\nabla\) be a classical linear connection on \(M\). We prove that the  well-known general connection \(\mathcal{F}(\Gamma,\nabla)\) in \(FY\to M\) is canonical with respect to fibred maps and with respect to natural transformations of bundle functors.


General connection; classical linear connection; fibred manifold; bundle functor; natural operator

Full Text:



Kobayashi, S., Nomizu, K., Foundations of Differential Geometry, Interscience Publishers, New York–London, 1963.

Kolar, I., Michor, P. W., Slovak, J., Natural Operations in Differential Geometry, Springer-Verlag, Berlin, 1993.

DOI: http://dx.doi.org/10.17951/a.2020.74.1.57-65
Date of publication: 2020-10-20 20:08:05
Date of submission: 2020-10-11 14:28:36


Total abstract view - 1028
Downloads (from 2020-06-17) - PDF - 545



  • There are currently no refbacks.

Copyright (c) 2020 Jan Kurek, Włodzimierz Mikulski