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Results tagged with connections
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user 3319
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].
20
votes
4
answers
3k
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Can a manifold have a curvature-free connection that is not torsion-free?
I know that in general curvature-free connections do not exist, and that in general torsion-free connections do. …
- 271
9
votes
2
answers
2k
views
Does every manifold have a flat connection?
Suppose I have a manifold and a vector bundle over it, but not a connection or a metric. Can I always find a connection on it that has a Riemann curvature tensor that is identically zero? If so, can I …
- 118k