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Concept information

mathematical technique > geometry > differential geometry > flat manifold

Terme préférentiel

flat manifold  

Définition(s)

  • In mathematics, a Riemannian manifold is said to be flat if its Riemann curvature tensor is everywhere zero. Intuitively, a flat manifold is one that "locally looks like" Euclidean space in terms of distances and angles, e.g. the interior angles of a triangle add up to 180°. The universal cover of a complete flat manifold is Euclidean space. This can be used to prove the theorem of Bieberbach (1911, 1912) that all compact flat manifolds are finitely covered by tori; the 3-dimensional case was proved earlier by Schoenflies (1891). (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Flat_manifold)

Concept(s) générique(s)

Synonyme(s)

  • flat metric

Traductions

URI

http://data.loterre.fr/ark:/67375/MDL-SH6P16LT-F

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