Natural transformations of connections on the first principal prolongation

Jan Vondra

Address: Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic


Abstract: We consider a vector bundle $E\rightarrow M$ and the principal bundle $PE$ of frames of $E$. We determine all natural transformations of the connection bundle of the first order principal prolongation of principal bundle $PE$ into itself.

AMSclassification: primary 53C05; secondary 58A32.

Keywords: natural bundle, gauge-natural bundle, natural operator, principal bundle, principal connection.

DOI: 10.5817/AM2014-1-21