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Ehresmann connections; covariant derivatives; connections on vector bundles, principal bundles, ∞-bundles, submersions, bundle gerbes; holonomy and higher holonomy; parallel transport; torsion; curvature. See also the tags [principal-bundles], [vector-bundles], [gerbes], [curvature], [geodesics], [characteristic-classes], [torsion].
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history of geometric mechanics
I was thinking about the foundations of geometric mechanics and its precursors.
I wondered who was the first to realized the equivalence between Riemannian geometry and Lagrangian mechanics. In parti …