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Results tagged with connections
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user 156492
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
Conceptual definition of the extension of a connection to 1-forms
Although the answer is already given, it may be helpful to point out how the coordinate definition contains the multilinear definition, in a single step of work. From the definition
$$(d^\nabla s)_{ij …
- 2,247
2
votes
1
answer
180
views
Vector field along an immersion whose covariant derivative is the differential
Let $(M,g)$ be a Riemannnian manifold and let $f:\Sigma\to M$ be a smooth immersion. Then the vector bundle $f^\ast TM\to\Sigma$ has a natural bundle metric and metric-compatible connection. Can one c …
- 2,247