We study the principal connections of the r-th principal prolongation W~rPof a principal bundle P (M, G) by using the related Lie algebroids. We deducethat both basic approaches to the concept of torsion are naturally equivalent.We prove that the torsion-free connections on W~rPare in bijection with thereductions of W~(r+1)Pto the groupG_m~1xG.Special attention is paid to theflow prolongation of connections.
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