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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.".
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- Covariant_derivative wikiPageLength "31329".
- Covariant_derivative wikiPageOutDegree "116".
- Covariant_derivative wikiPageRevisionID "701164810".
- Covariant_derivative wikiPageWikiLink Affine_connection.
- Covariant_derivative wikiPageWikiLink Basis_(linear_algebra).
- Covariant_derivative wikiPageWikiLink Category:Connection_(mathematics).
- Covariant_derivative wikiPageWikiLink Category:Differential_geometry.
- Covariant_derivative wikiPageWikiLink Category:Mathematical_methods_in_general_relativity.
- Covariant_derivative wikiPageWikiLink Category:Riemannian_geometry.
- Covariant_derivative wikiPageWikiLink Category:Solid_mechanics.
- Covariant_derivative wikiPageWikiLink Change_of_basis.
- Covariant_derivative wikiPageWikiLink Christoffel_symbols.
- Covariant_derivative wikiPageWikiLink Comma.
- Covariant_derivative wikiPageWikiLink Connection_(algebraic_framework).
- Covariant_derivative wikiPageWikiLink Connection_(mathematics).
- Covariant_derivative wikiPageWikiLink Connection_(principal_bundle).
- Covariant_derivative wikiPageWikiLink Connection_(vector_bundle).
- Covariant_derivative wikiPageWikiLink Connection_form.
- Covariant_derivative wikiPageWikiLink Coordinate_system.
- Covariant_derivative wikiPageWikiLink Cotangent_space.
- Covariant_derivative wikiPageWikiLink Covariance_and_contravariance_of_vectors.
- Covariant_derivative wikiPageWikiLink Covariant_transformation.
- Covariant_derivative wikiPageWikiLink Curvature_of_Riemannian_manifolds.
- Covariant_derivative wikiPageWikiLink Derivative.
- Covariant_derivative wikiPageWikiLink Differential_geometry.
- Covariant_derivative wikiPageWikiLink Differential_of_a_function.
- Covariant_derivative wikiPageWikiLink Differential_operator.
- Covariant_derivative wikiPageWikiLink Directional_derivative.
- Covariant_derivative wikiPageWikiLink Einstein_notation.
- Covariant_derivative wikiPageWikiLink Elwin_Bruno_Christoffel.
- Covariant_derivative wikiPageWikiLink Euclidean_space.
- Covariant_derivative wikiPageWikiLink Exterior_covariant_derivative.
- Covariant_derivative wikiPageWikiLink Foundations_of_Differential_Geometry.
- Covariant_derivative wikiPageWikiLink Gauge_covariant_derivative.
- Covariant_derivative wikiPageWikiLink Gauge_theory.
- Covariant_derivative wikiPageWikiLink Geodesic.
- Covariant_derivative wikiPageWikiLink Gregorio_Ricci-Curbastro.
- Covariant_derivative wikiPageWikiLink Hermann_Weyl.
- Covariant_derivative wikiPageWikiLink Introduction_to_the_mathematics_of_general_relativity.
- Covariant_derivative wikiPageWikiLink Jan_Arnoldus_Schouten.
- Covariant_derivative wikiPageWikiLink Jean-Louis_Koszul.
- Covariant_derivative wikiPageWikiLink John_Wiley_&_Sons.
- Covariant_derivative wikiPageWikiLink Levi-Civita_connection.
- Covariant_derivative wikiPageWikiLink Lie_algebra_cohomology.
- Covariant_derivative wikiPageWikiLink Lie_derivative.
- Covariant_derivative wikiPageWikiLink List_of_formulas_in_Riemannian_geometry.
- Covariant_derivative wikiPageWikiLink Manifold.
- Covariant_derivative wikiPageWikiLink Mathematics.
- Covariant_derivative wikiPageWikiLink Metric_tensor.
- Covariant_derivative wikiPageWikiLink Multilinear_map.
- Covariant_derivative wikiPageWikiLink One-form.
- Covariant_derivative wikiPageWikiLink Orthonormality.
- Covariant_derivative wikiPageWikiLink Parallel_transport.
- Covariant_derivative wikiPageWikiLink Partial_derivative.
- Covariant_derivative wikiPageWikiLink Principal_part.
- Covariant_derivative wikiPageWikiLink Product_rule.
- Covariant_derivative wikiPageWikiLink Projection_(linear_algebra).
- Covariant_derivative wikiPageWikiLink Pseudo-Riemannian_manifold.
- Covariant_derivative wikiPageWikiLink Ricci_calculus.
- Covariant_derivative wikiPageWikiLink Riemann_curvature_tensor.
- Covariant_derivative wikiPageWikiLink Riemannian_geometry.
- Covariant_derivative wikiPageWikiLink Section_(fiber_bundle).
- Covariant_derivative wikiPageWikiLink Semicolon.
- Covariant_derivative wikiPageWikiLink Smoothness.
- Covariant_derivative wikiPageWikiLink Tangent_bundle.
- Covariant_derivative wikiPageWikiLink Tangent_vector.
- Covariant_derivative wikiPageWikiLink Tangential_and_normal_components.
- Covariant_derivative wikiPageWikiLink Tensor.
- Covariant_derivative wikiPageWikiLink Tensor_(intrinsic_definition).
- Covariant_derivative wikiPageWikiLink Tensor_density.
- Covariant_derivative wikiPageWikiLink Tensor_derivative_(continuum_mechanics).
- Covariant_derivative wikiPageWikiLink Tensor_field.
- Covariant_derivative wikiPageWikiLink Tensor_product_of_modules.
- Covariant_derivative wikiPageWikiLink Torsion_tensor.
- Covariant_derivative wikiPageWikiLink Translation_(geometry).
- Covariant_derivative wikiPageWikiLink Tullio_Levi-Civita.
- Covariant_derivative wikiPageWikiLink Vector_bundle.
- Covariant_derivative wikiPageWikiLink Vector_calculus.
- Covariant_derivative wikiPageWikiLink Vector_field.
- Covariant_derivative wikiPageWikiLink Élie_Cartan.
- Covariant_derivative wikiPageWikiLinkText "''covariant'' divergence".
- Covariant_derivative wikiPageWikiLinkText "Christoffel symbol".
- Covariant_derivative wikiPageWikiLinkText "Covariant derivative".
- Covariant_derivative wikiPageWikiLinkText "Covariant derivative#Derivative along curve".
- Covariant_derivative wikiPageWikiLinkText "Covariant derivatives or differentials".
- Covariant_derivative wikiPageWikiLinkText "Koszul connection".
- Covariant_derivative wikiPageWikiLinkText "connection coefficients".
- Covariant_derivative wikiPageWikiLinkText "connection".
- Covariant_derivative wikiPageWikiLinkText "covariant derivative".
- Covariant_derivative wikiPageWikiLinkText "covariant derivatives".
- Covariant_derivative wikiPageWikiLinkText "covariant differential operator".
- Covariant_derivative wikiPageWikiLinkText "covariant differential".
- Covariant_derivative wikiPageWikiLinkText "covariant differentiation".
- Covariant_derivative wikiPageWikiLinkText "covariantly constant".
- Covariant_derivative wikiPageWikiLinkText "flat-space derivative operator".
- Covariant_derivative author "I.Kh. Sabitov".
- Covariant_derivative id "c/c026870".
- Covariant_derivative title "Covariant differentiation".