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Article

Mikulski, W. M.
Non-existence of natural operators transforming connections on $Y \to M$ into connections on $FY\to Y$. (English). Archivum Mathematicum, vol. 41 (2005), issue 1, pp. 1-4
MSC: 58A05, 58A20, 58A32 | MR 2142138 | Zbl 1112.58006
Keywords:
bundle functors; natural bundles; natural operators; connections
Summary:
Under some weak assumptions on a bundle functor $F:FM_{m,n}\rightarrow FM$ we prove that there is no $FM_{m,n}$-natural operator transforming connections on $Y\rightarrow M$ into connections on $FY\rightarrow Y$.
References:
[1] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry. Springer-Verlag, Berlin 1993. MR 1202431
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