Concept information
Preferred term
normal coordinate
Definition(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)
Broader concept(s)
In other languages
-
French
URI
http://data.loterre.fr/ark:/67375/MDL-RP6RTNVW-8
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