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Concept information

mathematical technique > algebra > tensor > curvature tensor > Ricci tensor

Terme préférentiel

Ricci tensor  

Définition(s)

  • In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space. The Ricci tensor can be characterized by measurement of how a shape is deformed as one moves along geodesics in the space. In general relativity, which involves the pseudo-Riemannian setting, this is reflected by the presence of the Ricci tensor in the Raychaudhuri equation. Partly for this reason, the Einstein field equations propose that spacetime can be described by a pseudo-Riemannian metric, with a strikingly simple relationship between the Ricci tensor and the matter content of the universe. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Ricci_curvature)

Concept(s) générique(s)

Synonyme(s)

  • Ricci curvature tensor

Traductions

URI

http://data.loterre.fr/ark:/67375/MDL-L32850JJ-W

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RDF/XML TURTLE JSON-LD Dernière modif. 24/04/2023