https://diffgeom.subwiki.org/w/index.php?action=history&feed=atom&title=Holonomy_of_a_loopHolonomy of a loop - Revision history2026-04-21T02:32:13ZRevision history for this page on the wikiMediaWiki 1.41.2https://diffgeom.subwiki.org/w/index.php?title=Holonomy_of_a_loop&diff=702&oldid=prevVipul: 1 revision2008-05-18T19:46:58Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://diffgeom.subwiki.org/w/index.php?title=Holonomy_of_a_loop&diff=701&oldid=prevVipul at 14:47, 1 September 20072007-09-01T14:47:03Z<p></p>
<p><b>New page</b></p><div>==Definition==<br />
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Let <math>M</math> be a [[differential manifold]], <math>E</math> a [[vector bundle]] over <math>M</math> and <math>\nabla</math> a [[connection]] on <math>E</math>. Let <math>m \in M</math> and <math>\gamma:[0,1]\to M</math> be a [[loop]] at <math>m</math> (viz <math>\gamma(0) = \gamma(1) = m</math>. The holonomy of <math>\gamma</math> is defined as the following linear transformation at <math>E_p</math>: it sends <math>v \in E_p</math> to the element <math>\phi_1(v)</math> where <math>\phi_t(v)</math> is the [[transport along a curve|transport]] of <math>v</math> along <math>\gamma</math>, with respect to the connection <math>\nabla</math>.<br />
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==Related notions==<br />
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* [[Holonomy group]]<br />
* [[Restricted holonomy group]]</div>Vipul