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Concept information

mathematical technique > geometry > differential geometry > conformally flat manifold

Terme préférentiel

conformally flat manifold  

Définition(s)

  • A (pseudo-)Riemannian manifold is conformally flat if each point has a neighborhood that can be mapped to flat space by a conformal transformation. In practice, the metric g of the manifold M has to be conformal to the flat metric η, i.e., the geodesics maintain in all points of M the angles by moving from one to the other, as well as keeping the null geodesics unchanged, that means exists a function λ(x) such that g(x) = λ²(x).η, where λ(x) is known as the conformal factor and x is a point on the manifold. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Conformally_flat_manifold)

Concept(s) générique(s)

Synonyme(s)

  • conformally flat metric

Traductions

URI

http://data.loterre.fr/ark:/67375/MDL-P811J1T3-Z

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