Acta Mathematica Sinica, English Series

, Volume 26, Issue 1, pp 169–184

Reduction theorems for principal and classical connections


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 operator reduction theorem principal prolongation 

MR(2000) Subject Classification

53C05 53C80 58A20 58A32 

Copyright information

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

Authors and Affiliations

  1. 1.Department of MathematicsBrno University of TechnologyBrnoCzech Republic
  2. 2.Institute of MathematicsJagiellonian UniversityKrakówPoland

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