Equivalent definitions for connections in higher order tangent bundles

Abstract

We establish a one to one correspondence between the\linebreak connections $C^{(k-1)}$ (in the bundle $%
T^{k}M\rightarrow M$, used by R. Miron in his work on higher order spaces) and $C^{(0)}$ (in the affine bundle $%
T^{k}M\rightarrow T^{k-1}M$, used for example in \cite{CSC1}).