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- 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.".
- Christoffel_symbols wikiPageExternalLink books?id=oTeGXkg0tn0C&pg=PA480.
- Christoffel_symbols wikiPageID "1401020".
- Christoffel_symbols wikiPageRevisionID "602474283".
- Christoffel_symbols hasPhotoCollection Christoffel_symbols.
- 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 type Artifact100021939.
- Christoffel_symbols type Conduit103089014.
- Christoffel_symbols type LorentzianManifolds.
- Christoffel_symbols type Manifold103717750.
- Christoffel_symbols type Object100002684.
- Christoffel_symbols type Passage103895293.
- Christoffel_symbols type PhysicalEntity100001930.
- Christoffel_symbols type Pipe103944672.
- Christoffel_symbols type Tube104493505.
- Christoffel_symbols type Way104564698.
- Christoffel_symbols type Whole100003553.
- Christoffel_symbols type YagoGeoEntity.
- Christoffel_symbols type YagoPermanentlyLocatedEntity.
- 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 label "Christoffelsymbole".
- Christoffel_symbols label "Christoffelsymbolen".
- Christoffel_symbols label "Simbolo di Christoffel".
- Christoffel_symbols label "Symbole Christoffela".
- Christoffel_symbols label "Symboles de Christoffel".
- Christoffel_symbols label "Símbolos de Christoffel".
- Christoffel_symbols label "Símbolos de Christoffel".
- Christoffel_symbols label "Символы Кристоффеля".
- Christoffel_symbols label "クリストッフェル記号".
- Christoffel_symbols label "克里斯托费尔符号".
- Christoffel_symbols sameAs Christoffelsymbole.
- Christoffel_symbols sameAs Símbolos_de_Christoffel.
- Christoffel_symbols sameAs Symboles_de_Christoffel.
- Christoffel_symbols sameAs Simbolo_di_Christoffel.
- Christoffel_symbols sameAs クリストッフェル記号.
- Christoffel_symbols sameAs 크리스토펠_기호.
- Christoffel_symbols sameAs Christoffelsymbolen.
- Christoffel_symbols sameAs Symbole_Christoffela.
- Christoffel_symbols sameAs Símbolos_de_Christoffel.
- Christoffel_symbols sameAs m.04zmmw.
- Christoffel_symbols sameAs Q847816.
- Christoffel_symbols sameAs Q847816.
- Christoffel_symbols sameAs Christoffel_symbols.
- Christoffel_symbols wasDerivedFrom Christoffel_symbols?oldid=602474283.
- Christoffel_symbols isPrimaryTopicOf Christoffel_symbols.