# Classification of principal connections naturally induced on $W^2PE$

## Jan Vondra

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

E-mail: vondra@math.muni.cz

Abstract: We consider a vector bundle $E\rightarrow M$ and the principal bundle $PE$ of frames of $E$. Let $K$ be a principal connection on $PE$ and let $\Lambda $ be a linear connection on $M$. We classify all principal connections on $W^2PE= P^2M\times _M J^2PE$ naturally given by $K$ and $\Lambda $.

AMSclassification: primary 53C05; secondary 53C10, 58A20, 58A32.

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