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Flat connection

156 bytes added, 22:01, 24 July 2011
Definition
===Symbol-free definition===
A [[defining ingredient::connection]] on a [[defining ingredient::vector bundle]] over a [[defining ingredient::differential manifold]] is said to be '''flat''' or '''integrable''' or '''curvature-free''' or '''locally flat''' if the [[defining ingredient::curvature of a connection|curvature of the connection ]] is zero everywhere.
===Definition with symbols===
===Definition in local coordinates===
In local coordinates, we require that the [[defining ingredient::curvature matrix of a connection|curvature matrix]] should vanish identically; in other words:
<math>\Omega := d\omega + \omega \wedge \omega = 0</math>
where <math>\omega</math> is the [[defining ingredient::matrix of connection forms]].
===Alternative definitions===
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