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- Cotton_tensor abstract "In differential geometry, the Cotton tensor on a (pseudo)-Riemannian manifold of dimension n is a third-order tensor concomitant of the metric, like the Weyl tensor. The vanishing of the Cotton tensor for n=3 is necessary and sufficient condition for the manifold to be conformally flat, as with the Weyl tensor for n≥4. For n<3 the Cotton tensor is identically zero. The concept is named after Émile Cotton.The proof of the classical result that for n = 3 the vanishing of the Cotton tensor is equivalent the metric being conformally flat is given by Eisenhart using a standard integrability argument. This tensor density is uniquely characterized by its conformal properties coupled with the demand that it be differentiable for arbitrary metrics, as shown by (Aldersley 1899).Recently, the study of three-dimensional spaces is becoming of great interest, because the Cotton tensor restricts the relation between the Ricci tensor and the energy-momentum tensor of matter in the Einstein equations and plays a important role in the Hamiltonian formalism of general relativity.".
- Cotton_tensor wikiPageExternalLink 0309008.
- Cotton_tensor wikiPageExternalLink fitem?id=AFST_1899_2_1_4_385_0.
- Cotton_tensor wikiPageID "1074140".
- Cotton_tensor wikiPageRevisionID "568007394".
- Cotton_tensor hasPhotoCollection Cotton_tensor.
- Cotton_tensor subject Category:Riemannian_geometry.
- Cotton_tensor subject Category:Tensors.
- Cotton_tensor subject Category:Tensors_in_general_relativity.
- Cotton_tensor type Abstraction100002137.
- Cotton_tensor type Cognition100023271.
- Cotton_tensor type Concept105835747.
- Cotton_tensor type Content105809192.
- Cotton_tensor type Idea105833840.
- Cotton_tensor type PsychologicalFeature100023100.
- Cotton_tensor type Quantity105855125.
- Cotton_tensor type Tensor105864481.
- Cotton_tensor type Tensors.
- Cotton_tensor type TensorsInGeneralRelativity.
- Cotton_tensor type Variable105857459.
- Cotton_tensor comment "In differential geometry, the Cotton tensor on a (pseudo)-Riemannian manifold of dimension n is a third-order tensor concomitant of the metric, like the Weyl tensor. The vanishing of the Cotton tensor for n=3 is necessary and sufficient condition for the manifold to be conformally flat, as with the Weyl tensor for n≥4. For n<3 the Cotton tensor is identically zero.".
- Cotton_tensor label "Cotton tensor".
- Cotton_tensor label "Tenseur de Cotton-York".
- Cotton_tensor label "Тензор Коттона".
- Cotton_tensor label "コットンテンソル".
- Cotton_tensor sameAs Tenseur_de_Cotton-York.
- Cotton_tensor sameAs コットンテンソル.
- Cotton_tensor sameAs m.043nws.
- Cotton_tensor sameAs Q3518152.
- Cotton_tensor sameAs Q3518152.
- Cotton_tensor sameAs Cotton_tensor.
- Cotton_tensor wasDerivedFrom Cotton_tensor?oldid=568007394.
- Cotton_tensor isPrimaryTopicOf Cotton_tensor.