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Doupovec, Miroslav; Mikulski, Włodzimierz M.

On the existence of prolongation of connections. (English) Zbl 1164.58300

Czech. Math. J. 56, No. 4, 1323-1334 (2006).
Summary: We classify all bundle functors \(G\) admitting natural operators transforming connections on a fibered manifold \(Y\to M\) into connections on \(GY\to M\). Then we solve a similar problem for natural operators transforming connections on \(Y\to M\) into connections on \(GY\to Y\).

Cited in 3 Documents

MSC:

58A05 Differentiable manifolds, foundations
58A20 Jets in global analysis

Keywords:

bundle functor; connection; natural operator
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\textit{M. Doupovec} and \textit{W. M. Mikulski}, Czech. Math. J. 56, No. 4, 1323--1334 (2006; Zbl 1164.58300)
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References:

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[2] M. Doupovec and I. Koláč: Iteration of fiber product preserving bundle functors. Monatshefte Math. 134 (2001), 39–50. · Zbl 0999.58001 · doi:10.1007/s006050170010
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[9] W. M. Mikulski: Non-existence of natural operators transforming connections on Y M into connections on FY Y. Arch. Math. (Brno) 41 (2005), 1–4. · Zbl 1112.58006
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