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The contorsion tensor in differential geometry is the difference between a connection with and without torsion in it. It commonly appears in the study of spin connections. Thus, for example, a vielbein together with a spin connection, when subject to the condition of vanishing torsion, gives a description of Einstein gravity. For supersymmetry, the same constraint, of vanishing torsion, gives (the field equations of) 11-dimensional supergravity. That is, the contorsion tensor, along with the connection, becomes one of the dynamical objects of the theory, demoting the metric to a secondary, derived role.

Attributes	Values
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rdfs:label	Contorsion tensor (en)
rdfs:comment	The contorsion tensor in differential geometry is the difference between a connection with and without torsion in it. It commonly appears in the study of spin connections. Thus, for example, a vielbein together with a spin connection, when subject to the condition of vanishing torsion, gives a description of Einstein gravity. For supersymmetry, the same constraint, of vanishing torsion, gives (the field equations of) 11-dimensional supergravity. That is, the contorsion tensor, along with the connection, becomes one of the dynamical objects of the theory, demoting the metric to a secondary, derived role. (en)
dcterms:subject	Riemannian geometry Tensors Connection (mathematics)
Wikipage page ID	1561997 (xsd:integer)
Wikipage revision ID	990100002 (xsd:integer)
Link from a Wikipage to another Wikipage	Belinfante–Rosenfeld stress–energy tensor Metric connection Torsion form Ehresmann connection Connection (vector bundle) Levi-Civita connection Spin connection Affine connection Fiber bundle Teleparallelism Riemannian geometry Tensors Affine geometry Connection (mathematics) Supergravity Tautological one-form Torsion tensor Differential geometry Field equation Metric geometry Linear form Cartan's equivalence method Vertical and horizontal bundles Supersymmetry Supermanifold Solder form Vielbein Christoffel symbol Weitzenböck connection
sameAs	Contorsion tensor Contorsion tensor Contorsion tensor Contorsion tensor
dbp:wikiPageUsesTemplate	dbt:Reflist
has abstract	The contorsion tensor in differential geometry is the difference between a connection with and without torsion in it. It commonly appears in the study of spin connections. Thus, for example, a vielbein together with a spin connection, when subject to the condition of vanishing torsion, gives a description of Einstein gravity. For supersymmetry, the same constraint, of vanishing torsion, gives (the field equations of) 11-dimensional supergravity. That is, the contorsion tensor, along with the connection, becomes one of the dynamical objects of the theory, demoting the metric to a secondary, derived role. The elimination of torsion in a connection is referred to as the absorption of torsion, and is one of the steps of Cartan's equivalence method for establishing the equivalence of geometric structures. (en)
prov:wasDerivedFrom	wikipedia-en:Contorsion_tensor?oldid=990100002&ns=0
page length (characters) of wiki page	9757 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Contorsion_tensor
is Link from a Wikipage to another Wikipage of	Metric-affine gravitation theory Metric connection Index of physics articles (C) Connection form Christoffel symbols Fundamental theorem of Riemannian geometry Boyer–Lindquist coordinates Connection (vector bundle) Spin connection Einstein–Cartan theory Torsion tensor Contortion (disambiguation) Contortion tensor Vertical and horizontal bundles Solder form Contorsion form
is Wikipage redirect of	Contortion tensor Contorsion form
is foaf:primaryTopic of	wikipedia-en:Contorsion_tensor

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