Acta Mathematica Sinica, English Series

, Volume 26, Issue 1, pp 169–184

Reduction theorems for principal and classical connections

Article

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

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.

Keywords

Gauge natural operatorreduction theoremprincipal prolongation

MR(2000) Subject Classification

53C0553C8058A2058A32

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