Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Christoffel_symbols> ?p ?o }
- Christoffel_symbols abstract "In mathematics and physics, the Christoffel symbols, named for Elwin Bruno Christoffel (1829–1900), are numerical arrays of real numbers that describe, in coordinates, the effects of parallel transport in curved surfaces and, more generally, manifolds. As such, they are coordinate-space expressions for the Levi-Civita connection derived from the metric tensor. In a broader sense, the connection coefficients of an arbitrary (not necessarily metric) affine connection in a coordinate basis are also called Christoffel symbols. The Christoffel symbols may be used for performing practical calculations in differential geometry. For example, the Riemann curvature tensor can be expressed entirely in terms of the Christoffel symbols and their first partial derivatives.At each point of the underlying n-dimensional manifold, for any local coordinate system, the Christoffel symbol is an array with three dimensions: n × n × n. Each of the n3 components is a real number.Under linear coordinate transformations on the manifold, its components transform like those of a tensor, but under general coordinate transformations, they do not. In many practical problems, most components of the Christoffel symbols are equal to zero, provided the coordinate system and the metric tensor possess some common symmetries.In general relativity, the Christoffel symbol plays the role of the gravitational force field with the corresponding gravitational potential being the metric tensor.".
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- Christoffel_symbols wikiPageID "1401020".
- Christoffel_symbols wikiPageLength "20025".
- Christoffel_symbols wikiPageOutDegree "83".
- Christoffel_symbols wikiPageRevisionID "677789954".
- Christoffel_symbols wikiPageWikiLink 0_(number).
- Christoffel_symbols wikiPageWikiLink Affine_connection.
- Christoffel_symbols wikiPageWikiLink Atlas_(topology).
- Christoffel_symbols wikiPageWikiLink Basic_introduction_to_the_mathematics_of_curved_spacetime.
- Christoffel_symbols wikiPageWikiLink Basis_(linear_algebra).
- Christoffel_symbols wikiPageWikiLink Basis_of_a_vector_space.
- Christoffel_symbols wikiPageWikiLink Category:Connection_(mathematics).
- Christoffel_symbols wikiPageWikiLink Category:Lorentzian_manifolds.
- Christoffel_symbols wikiPageWikiLink Category:Mathematical_notation.
- Christoffel_symbols wikiPageWikiLink Category:Mathematical_physics.
- Christoffel_symbols wikiPageWikiLink Category:Riemannian_geometry.
- Christoffel_symbols wikiPageWikiLink Classical_treatment_of_tensors.
- Christoffel_symbols wikiPageWikiLink Commutator.
- Christoffel_symbols wikiPageWikiLink Coordinate_system.
- Christoffel_symbols wikiPageWikiLink Coordinate_transformations.
- Christoffel_symbols wikiPageWikiLink Course_of_Theoretical_Physics.
- Christoffel_symbols wikiPageWikiLink Covariance_and_contravariance_of_vectors.
- Christoffel_symbols wikiPageWikiLink Covariant_derivative.
- Christoffel_symbols wikiPageWikiLink Covector.
- Christoffel_symbols wikiPageWikiLink Deriving_the_Schwarzschild_solution.
- Christoffel_symbols wikiPageWikiLink Differentiable_manifold.
- Christoffel_symbols wikiPageWikiLink Differential_geometry.
- Christoffel_symbols wikiPageWikiLink Dover_Publications.
- Christoffel_symbols wikiPageWikiLink Einstein_field_equations.
- Christoffel_symbols wikiPageWikiLink Einstein_notation.
- Christoffel_symbols wikiPageWikiLink Elwin_Bruno_Christoffel.
- Christoffel_symbols wikiPageWikiLink Gauss–Codazzi_equations.
- Christoffel_symbols wikiPageWikiLink General_relativity.
- Christoffel_symbols wikiPageWikiLink Holonomic_basis.
- Christoffel_symbols wikiPageWikiLink Introduction_to_the_mathematics_of_general_relativity.
- Christoffel_symbols wikiPageWikiLink Jet_bundle.
- Christoffel_symbols wikiPageWikiLink Kronecker_delta.
- Christoffel_symbols wikiPageWikiLink Levi-Civita_connection.
- Christoffel_symbols wikiPageWikiLink Lie_derivative.
- Christoffel_symbols wikiPageWikiLink Linear_form.
- Christoffel_symbols wikiPageWikiLink List_of_formulas_in_Riemannian_geometry.
- Christoffel_symbols wikiPageWikiLink Local_coordinate_system.
- Christoffel_symbols wikiPageWikiLink Lorentz_manifold.
- Christoffel_symbols wikiPageWikiLink Manifold.
- Christoffel_symbols wikiPageWikiLink Mathematics.
- Christoffel_symbols wikiPageWikiLink Matrix_(mathematics).
- Christoffel_symbols wikiPageWikiLink Metric_tensor.
- Christoffel_symbols wikiPageWikiLink Mixed_tensor.
- Christoffel_symbols wikiPageWikiLink Nabla_symbol.
- Christoffel_symbols wikiPageWikiLink Normal_coordinates.
- Christoffel_symbols wikiPageWikiLink Parallel_transport.
- Christoffel_symbols wikiPageWikiLink Partial_derivative.
- Christoffel_symbols wikiPageWikiLink Physics.
- Christoffel_symbols wikiPageWikiLink Proofs_involving_Christoffel_symbols.
- Christoffel_symbols wikiPageWikiLink Proofs_involving_covariant_derivatives.
- Christoffel_symbols wikiPageWikiLink Pseudo-Riemannian_manifold.
- Christoffel_symbols wikiPageWikiLink Pullback_(differential_geometry).
- Christoffel_symbols wikiPageWikiLink Pushforward_(differential).
- Christoffel_symbols wikiPageWikiLink Real_number.
- Christoffel_symbols wikiPageWikiLink Ricci_calculus.
- Christoffel_symbols wikiPageWikiLink Ricci_curvature.
- Christoffel_symbols wikiPageWikiLink Ricci_tensor.
- Christoffel_symbols wikiPageWikiLink Riemann_curvature_tensor.
- Christoffel_symbols wikiPageWikiLink Riemannian_geometry.
- Christoffel_symbols wikiPageWikiLink Riemannian_manifold.
- Christoffel_symbols wikiPageWikiLink Riemann–Christoffel_tensor.
- Christoffel_symbols wikiPageWikiLink Sign_convention.
- Christoffel_symbols wikiPageWikiLink Solving_the_geodesic_equations.
- Christoffel_symbols wikiPageWikiLink Spacetime.
- Christoffel_symbols wikiPageWikiLink Surface.
- Christoffel_symbols wikiPageWikiLink Tangent_space.
- Christoffel_symbols wikiPageWikiLink Tensor.
- Christoffel_symbols wikiPageWikiLink Torsion_tensor.
- Christoffel_symbols wikiPageWikiLink Vector_field.
- Christoffel_symbols wikiPageWikiLink Vector_fields.
- Christoffel_symbols wikiPageWikiLink Vector_fields_in_cylindrical_and_spherical_coordinates.
- Christoffel_symbols wikiPageWikiLink Vector_space.
- Christoffel_symbols wikiPageWikiLinkText "Affine connection".
- Christoffel_symbols wikiPageWikiLinkText "Christoffel symbol of the second kind".
- Christoffel_symbols wikiPageWikiLinkText "Christoffel symbol".
- Christoffel_symbols wikiPageWikiLinkText "Christoffel symbols".
- Christoffel_symbols wikiPageWikiLinkText "second kind".
- Christoffel_symbols hasPhotoCollection Christoffel_symbols.
- Christoffel_symbols wikiPageUsesTemplate Template:Citation.
- Christoffel_symbols wikiPageUsesTemplate Template:Cite_book.
- Christoffel_symbols wikiPageUsesTemplate Template:Reflist.
- Christoffel_symbols wikiPageUsesTemplate Template:Tensors.
- Christoffel_symbols subject Category:Connection_(mathematics).
- Christoffel_symbols subject Category:Lorentzian_manifolds.
- Christoffel_symbols subject Category:Mathematical_notation.
- Christoffel_symbols subject Category:Mathematical_physics.
- Christoffel_symbols subject Category:Riemannian_geometry.
- Christoffel_symbols hypernym Arrays.
- Christoffel_symbols type Article.
- Christoffel_symbols type Article.
- Christoffel_symbols type Physic.
- Christoffel_symbols comment "In mathematics and physics, the Christoffel symbols, named for Elwin Bruno Christoffel (1829–1900), are numerical arrays of real numbers that describe, in coordinates, the effects of parallel transport in curved surfaces and, more generally, manifolds. As such, they are coordinate-space expressions for the Levi-Civita connection derived from the metric tensor.".
- Christoffel_symbols label "Christoffel symbols".
- Christoffel_symbols sameAs Christoffelsymbole.