Quantum defect: Difference between revisions

Latest revision as of 01:25, 24 August 2014

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-In [[mathematics]], a '''coframe''' or '''coframe field''' on a [[smooth manifold]] <math>M</math> is a system of [[one-form]]s or [[covector]]s which form a [[vector space|basis]] of the [[cotangent bundle]] at every point.  In the exterior algebra of <math>M</math>, one has a natural map from <math>v_k:\bigoplus^kT^*M\to\bigwedge^kT^*M</math>, given by <math>v_k:(\rho_1,\ldots,\rho_k)\mapsto \rho_1\wedge\ldots\wedge\rho_k</math>.  If <math>M</math> is <math>n</math> dimensional a coframe is given by a section <math>\sigma</math> of <math>\bigoplus^nT^*M</math> such that <math>v_n\circ\sigma\neq 0</math>.  The inverse image under <math>v_n</math> of the complement of the zero section of <math>\bigwedge^nT^*M</math> forms a <math>GL(n)</math> [[principal bundle]] over <math>M</math>, which is called the [[frame bundle|coframe bundle]].
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-== See also ==
-* [[Frame fields in general relativity]]
-* [[Moving frame]]
-[[Category:Differential geometry]]
-{{differential-geometry-stub}}

Quantum defect: Difference between revisions

Latest revision as of 01:25, 24 August 2014

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