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Results tagged with connections
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user 17047
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].
18
votes
3
answers
4k
views
Formal adjoint of the covariant derivative
I can see where it steams from for metric connections, but not for arbitary $\nabla$. Is this forumla just taken as a generalization of the compatible case? …
- 5,824
7
votes
1
answer
1k
views
Differential forms along the fiber
Let $E \to M$ be a smooth fiber bundle. Instead of differential forms defined on the whole tangent bundle $TE$ one could also consider forms on the vertical tangent bundle $VE$, i.e. forms defined on …
- 5,824