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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 wikiPageLength "5933".
- Normal_coordinates wikiPageOutDegree "41".
- Normal_coordinates wikiPageRevisionID "636859544".
- Normal_coordinates wikiPageWikiLink Affine_connection.
- Normal_coordinates wikiPageWikiLink Albert_Einstein.
- Normal_coordinates wikiPageWikiLink Atlas_(topology).
- Normal_coordinates wikiPageWikiLink Basis_(linear_algebra).
- Normal_coordinates wikiPageWikiLink Basis_of_a_vector_space.
- Normal_coordinates wikiPageWikiLink Block_diagonal.
- Normal_coordinates wikiPageWikiLink Block_matrix.
- Normal_coordinates wikiPageWikiLink Category:Coordinate_systems_in_differential_geometry.
- Normal_coordinates wikiPageWikiLink Category:Riemannian_geometry.
- Normal_coordinates wikiPageWikiLink Christoffel_symbols.
- Normal_coordinates wikiPageWikiLink Diffeomorphism.
- Normal_coordinates wikiPageWikiLink Differentiable_manifold.
- Normal_coordinates wikiPageWikiLink Differential_geometry.
- Normal_coordinates wikiPageWikiLink Equivalence_principle.
- Normal_coordinates wikiPageWikiLink Exponential_map_(Riemannian_geometry).
- Normal_coordinates wikiPageWikiLink Fermi_coordinates.
- Normal_coordinates wikiPageWikiLink Finsler_manifold.
- Normal_coordinates wikiPageWikiLink Foundations_of_Differential_Geometry.
- Normal_coordinates wikiPageWikiLink Gausss_lemma_(Riemannian_geometry).
- Normal_coordinates wikiPageWikiLink General_relativity.
- Normal_coordinates wikiPageWikiLink General_theory_of_relativity.
- Normal_coordinates wikiPageWikiLink Geodesic.
- Normal_coordinates wikiPageWikiLink Gradient.
- Normal_coordinates wikiPageWikiLink Inertial_frame.
- Normal_coordinates wikiPageWikiLink Inertial_frame_of_reference.
- Normal_coordinates wikiPageWikiLink John_Wiley_&_Sons.
- Normal_coordinates wikiPageWikiLink Kronecker_delta.
- Normal_coordinates wikiPageWikiLink Levi-Civita_connection.
- Normal_coordinates wikiPageWikiLink Local_coordinate_system.
- Normal_coordinates wikiPageWikiLink Local_reference_frame.
- Normal_coordinates wikiPageWikiLink Mathematische_Annalen.
- Normal_coordinates wikiPageWikiLink Metric_tensor.
- Normal_coordinates wikiPageWikiLink N-sphere.
- Normal_coordinates wikiPageWikiLink N_sphere.
- Normal_coordinates wikiPageWikiLink Neighborhood_(mathematics).
- Normal_coordinates wikiPageWikiLink Neighbourhood_(mathematics).
- Normal_coordinates wikiPageWikiLink Orthonormal_basis.
- Normal_coordinates wikiPageWikiLink Partial_derivative.
- Normal_coordinates wikiPageWikiLink Pseudo-Riemannian.
- Normal_coordinates wikiPageWikiLink Pseudo-Riemannian_manifold.
- Normal_coordinates wikiPageWikiLink Riemannian_manifold.
- Normal_coordinates wikiPageWikiLink Spherical_coordinate_system.
- Normal_coordinates wikiPageWikiLink Spherical_coordinates.
- Normal_coordinates wikiPageWikiLink Tangent_space.
- Normal_coordinates wikiPageWikiLink Torsion_tensor.
- Normal_coordinates wikiPageWikiLink Wiley_Interscience.
- Normal_coordinates wikiPageWikiLinkText "Normal coordinates".
- Normal_coordinates wikiPageWikiLinkText "normal coordinate system".
- Normal_coordinates wikiPageWikiLinkText "normal coordinates".
- Normal_coordinates hasPhotoCollection Normal_coordinates.
- Normal_coordinates wikiPageUsesTemplate Template:Citation.
- Normal_coordinates wikiPageUsesTemplate Template:Harv.
- Normal_coordinates subject Category:Coordinate_systems_in_differential_geometry.
- Normal_coordinates subject Category:Riemannian_geometry.
- 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 "Normal coordinates".
- 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 wasDerivedFrom Normal_coordinates?oldid=636859544.
- Normal_coordinates isPrimaryTopicOf Normal_coordinates.