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Results tagged with connections
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user 8446
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].
23
votes
4
answers
5k
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Why is it important that partial derivatives commute?
I am asking this in the context of differential geometry (specifically Riemannian).
When the Levi-Civita Connection is defined, we require that the torsion tensor is 0, which in local coordinates tra …
- 995
19
votes
6
answers
9k
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Tensor contraction and Covariant Derivative
In addition, I see that one of the requirements for a covariant derivative (in the context of connections) is to commute with contraction. …
- 995