In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [F. Dumitrescu, Journal of Homotopy and Related Structures, vol 5, no 1 (2010)] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new approach to connections on a bundle as a consistent way to lift the dynamics of the manifold to the bundle.
Cite this article
Florin Dumitrescu, Another Look at Connections. Rend. Sem. Mat. Univ. Padova 127 (2012), pp. 99–105DOI 10.4171/RSMUP/127-6