Acta Mathematica Sinica, English Series

, Volume 26, Issue 1, pp 169–184

Reduction theorems for principal and classical connections


    • Department of MathematicsBrno University of Technology
  • Włodzimierz M. Mikulski
    • Institute of MathematicsJagiellonian University

DOI: 10.1007/s10114-010-7333-2

Cite this article as:
Doupovec, M. & Mikulski, W.M. Acta. Math. Sin.-English Ser. (2010) 26: 169. doi:10.1007/s10114-010-7333-2


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.


Gauge natural operatorreduction theoremprincipal prolongation

MR(2000) Subject Classification


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© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer Berlin Heidelberg 2010