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Concept information

mathematical technique > geometry > differential geometry > normal coordinate
mathematical technique > frame of reference > coordinate system > normal coordinate
astronomical technique > astrometry > coordinate system > normal coordinate

Terme préférentiel

normal coordinate  

Définition(s)

  • In differential geometry, normal coordinates at a point p in a differentiable manifold equipped with a symmetric affine connection are a local coordinate system in a neighborhood of p obtained by applying the exponential map to the tangent space at p. In a normal coordinate system, the Christoffel symbols of the connection vanish at the point p, thus often simplifying local calculations. In normal coordinates associated to the Levi-Civita connection of a Riemannian manifold, one can additionally arrange that the metric tensor is the Kronecker delta at the point p, and that the first partial derivatives of the metric at p vanish. (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Normal_coordinates)

Concept(s) générique(s)

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URI

http://data.loterre.fr/ark:/67375/MDL-RP6RTNVW-8

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