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Concept information

geometry > differential geometry > Riemannian geometry > Cotton tensor
mathematical physics > general relativity > Cotton tensor

Terme préférentiel

Cotton tensor  

Définition(s)

  • In differential geometry, the Cotton tensor on a (pseudo)-Riemannian manifold of dimension n is a third-order tensor concomitant of the metric. The vanishing of the Cotton tensor for n = 3 is necessary and sufficient condition for the manifold to be conformally flat. By contrast, in dimensions n ≥ 4, the vanishing of the Cotton tensor is necessary but not sufficient for the metric to be conformally flat; instead, the corresponding necessary and sufficient condition in these higher dimensions is the vanishing of the Weyl tensor, while the Cotton tensor just becomes a constant times the divergence of the Weyl tensor. For n < 3 the Cotton tensor is identically zero. The concept is named after Émile Cotton.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Cotton_tensor)

Concept(s) générique(s)

Traductions

URI

http://data.loterre.fr/ark:/67375/PSR-ZBFG6F81-J

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RDF/XML TURTLE JSON-LD Dernière modif. 08/08/2023