Restricted holonomy group - Revision history

Vipul: 2 revisions

2008-05-18T19:51:38Z

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2007-09-01T15:06:24Z

Facts

← Older revision		Revision as of 15:06, 1 September 2007
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	==Facts==		==Facts==

	The restricted holonomy group is a subgroup of the [[holonomy group]], which comprises all the linear transformations that occur as the [[holonomy of a loop]] (not necessarily homotopic to the constant loop).		The restricted holonomy group is a [[normal subgroup]] of the [[holonomy group]], which comprises all the linear transformations that occur as the [[holonomy of a loop]] (not necessarily homotopic to the constant loop).

Vipul at 15:03, 1 September 2007

2007-09-01T15:03:58Z

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==Definition==

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>. The '''restricted holonomy group''' at <math>m \in M</math> is defined as the subgroup of <math>GL(E_m)</math> comprising all those linear transformations that occur as the [[holonomy of a loop]] that is homotopic to the constant loop.

==Facts==

The restricted holonomy group is a subgroup of the [[holonomy group]], which comprises all the linear transformations that occur as the [[holonomy of a loop]] (not necessarily homotopic to the constant loop).