On naturality of some construction of connections

Jan Kurek, Włodzimierz Mikulski

Abstract


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.

Keywords


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

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References


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
Data publikacji: 2020-10-20 20:08:05
Data złożenia artykułu: 2020-10-11 14:28:36


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