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Another look at connections. (English) Zbl 1246.53018

Summary: In this note we make use of some properties of vector fields on a manifold to give an alternate proof 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.

MSC:

53B05 Linear and affine connections
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References:

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