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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].

3 votes

Is there a way to define a Lie derivative of a connection?

I was expecting the Lie derivative of a connection to be another connection but Vladimir's answer about the difference of two connections being a tensor makes a lot of sense. …
Luis Felipe López Reyes's user avatar