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- Covariant_derivative abstract "In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection. In the special case of a manifold isometrically embedded into a higher-dimensional Euclidean space, the covariant derivative can be viewed as the orthogonal projection of the Euclidean derivative along a tangent vector onto the manifold's tangent space. In this case the Euclidean derivative is broken into two parts, the extrinsic normal component and the intrinsic covariant derivative component.This article presents an introduction to the covariant derivative of a vector field with respect to a vector field, both in a coordinate free language and using a local coordinate system and the traditional index notation. The covariant derivative of a tensor field is presented as an extension of the same concept. The covariant derivative generalizes straightforwardly to a notion of differentiation associated to a connection on a vector bundle, also known as a Koszul connection.".
- Covariant_derivative wikiPageID "431848".
- Covariant_derivative wikiPageRevisionID "606507610".
- Covariant_derivative author "I.Kh. Sabitov".
- Covariant_derivative hasPhotoCollection Covariant_derivative.
- Covariant_derivative id "c/c026870".
- Covariant_derivative title "Covariant differentiation".
- Covariant_derivative subject Category:Connection_(mathematics).
- Covariant_derivative subject Category:Differential_geometry.
- Covariant_derivative subject Category:Mathematical_methods_in_general_relativity.
- Covariant_derivative subject Category:Riemannian_geometry.
- Covariant_derivative subject Category:Solid_mechanics.
- Covariant_derivative type Ability105616246.
- Covariant_derivative type Abstraction100002137.
- Covariant_derivative type Cognition100023271.
- Covariant_derivative type Know-how105616786.
- Covariant_derivative type MathematicalMethodsInGeneralRelativity.
- Covariant_derivative type Method105660268.
- Covariant_derivative type PsychologicalFeature100023100.
- Covariant_derivative comment "In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a differential operator, to be contrasted with the approach given by a principal connection on the frame bundle – see affine connection.".
- Covariant_derivative label "Covariant derivative".
- Covariant_derivative label "Covariante afgeleide".
- Covariant_derivative label "Derivada covariante".
- Covariant_derivative label "Derivada covariante".
- Covariant_derivative label "Derivata covariante".
- Covariant_derivative label "Dérivée covariante".
- Covariant_derivative label "Pochodna kowariantna".
- Covariant_derivative label "Ковариантная производная".
- Covariant_derivative label "共变导数".
- Covariant_derivative sameAs Derivada_covariante.
- Covariant_derivative sameAs Dérivée_covariante.
- Covariant_derivative sameAs Derivata_covariante.
- Covariant_derivative sameAs Covariante_afgeleide.
- Covariant_derivative sameAs Pochodna_kowariantna.
- Covariant_derivative sameAs Derivada_covariante.
- Covariant_derivative sameAs m.027s33.
- Covariant_derivative sameAs Q2287715.
- Covariant_derivative sameAs Q2287715.
- Covariant_derivative sameAs Covariant_derivative.
- Covariant_derivative wasDerivedFrom Covariant_derivative?oldid=606507610.
- Covariant_derivative isPrimaryTopicOf Covariant_derivative.