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- Normal_coordinates abstract "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.A basic result of differential geometry states that normal coordinates at a point always exist on a manifold with a symmetric affine connection. In such coordinates the covariant derivative reduces to a partial derivative (at p only), and the geodesics through p are locally linear functions of t (the affine parameter). This idea was implemented in a fundamental way by Albert Einstein in the general theory of relativity: the equivalence principle uses normal coordinates via inertial frames. Normal coordinates always exist for the Levi-Civita connection of a Riemannian or Pseudo-Riemannian manifold. By contrast, there is no way to define normal coordinates for Finsler manifolds (Busemann 1955).".
- Normal_coordinates wikiPageID "7679762".
- Normal_coordinates wikiPageRevisionID "544577827".
- Normal_coordinates hasPhotoCollection Normal_coordinates.
- Normal_coordinates subject Category:Coordinate_systems_in_differential_geometry.
- Normal_coordinates subject Category:Riemannian_geometry.
- Normal_coordinates type Abstraction100002137.
- Normal_coordinates type Arrangement105726596.
- Normal_coordinates type Cognition100023271.
- Normal_coordinates type CoordinateSystem105728024.
- Normal_coordinates type CoordinateSystemsInDifferentialGeometry.
- Normal_coordinates type PsychologicalFeature100023100.
- Normal_coordinates type Structure105726345.
- Normal_coordinates comment "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.".
- Normal_coordinates label "Coordonnées normales".
- Normal_coordinates label "Normal coordinates".
- Normal_coordinates label "Riemannsche Normalkoordinaten".
- Normal_coordinates sameAs Riemannsche_Normalkoordinaten.
- Normal_coordinates sameAs Coordonnées_normales.
- Normal_coordinates sameAs m.0268pbk.
- Normal_coordinates sameAs Q2152232.
- Normal_coordinates sameAs Q2152232.
- Normal_coordinates sameAs Normal_coordinates.
- Normal_coordinates wasDerivedFrom Normal_coordinates?oldid=544577827.
- Normal_coordinates isPrimaryTopicOf Normal_coordinates.