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Reduction theorems for principal and classical connections

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Abstract

We prove general reduction theorems for gauge natural operators transforming principal connections and classical linear connections on the base manifold into sections of an arbitrary gauge natural bundle. Then we apply our results to the principal prolongation of connections. Finally we describe all such gauge natural operators for some special cases of a Lie group G.

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Authors and Affiliations

  1. Department of Mathematics, Brno University of Technology, Technická 2, 616 69, Brno, Czech Republic

    Miroslav Doupovec

  2. Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, Kraków, Poland

    Włodzimierz M. Mikulski

Authors
  1. Miroslav Doupovec
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  2. Włodzimierz M. Mikulski
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Correspondence to Miroslav Doupovec.

Additional information

The first author is supported by the Ministry of Education of Czech Republic under the project MSM 0021630518

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Doupovec, M., Mikulski, W.M. Reduction theorems for principal and classical connections. Acta. Math. Sin.-English Ser. 26, 169–184 (2010). https://doi.org/10.1007/s10114-010-7333-2

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  • DOI: https://doi.org/10.1007/s10114-010-7333-2

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