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Results tagged with connections
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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].
29
votes
4
answers
4k
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Rolling without slipping interpretation of torsion
This is, in a sense, a follow up to this question.
Hehl and Obukhov try to give an intuitive description of torsion. I am confused about their description. I am looking at the following paragraph on p …
- 156k
7
votes
4
answers
423
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Hamiltonians which commute both as operators and as connections
.$$
For those who don't like the language of connections, we can expand $(\dagger)$ as $\partial H_i/\partial t_j - \partial H_j/\partial t_i + [H_i, H_j]=0$ or, in the presence of $(\ast)$, as
$$\frac …
- 156k
3
votes
2
answers
502
views
Kernel of an integrable holomorphic dee-bar connection is a holomorphic vector bundle
The analogous fact for smooth connections is (one direction of) the Riemann-Hilbert correspondence; see, for example, Theorem 2.6 here. …
- 156k