Rendiconti del Seminario Matematico della Università di Padova

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Volume 127, 2012, pp. 99–105
DOI: 10.4171/RSMUP/127-6

Another Look at Connections

Florin Dumitrescu[1]

(1) Institute of Mathematics “Simion Stoilow”, Romanian Academy, 21 Calea Grivitei, 010702, Bucharest, Romania

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.

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Dumitrescu Florin: Another Look at Connections. Rend. Sem. Mat. Univ. Padova 127 (2012), 99-105. doi: 10.4171/RSMUP/127-6