Gauge natural prolongation of connections

Volume 95 / 2009

Miroslav Doupovec, W/lodzimierz M. Mikulski Annales Polonici Mathematici 95 (2009), 37-50 MSC: 58A05, 58A20. DOI: 10.4064/ap95-1-3


The main result is the classification of all gauge bundle functors $H$ on the category ${\cal P}{\cal B}_m(G)$ which admit gauge natural operators transforming principal connections on $P\to M$ into general connections on $HP\to M$. We also describe all gauge natural operators of this type. Similar problems are solved for the prolongation of principal connections to $HP\to P$. A special attention is paid to linear connections.


  • Miroslav DoupovecDepartment of Mathematics
    Brno University of Technology
    FSI VUT Brno, Technická 2
    616 69 Brno, Czech Republic
  • W/lodzimierz M. MikulskiInstitute of Mathematics
    Jagiellonian University
    /Lojasiewicza 6
    30-348 Kraków, Poland

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