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- Pullback_(differential_geometry) abstract "Suppose that φ:M→ N is a smooth map between smooth manifolds M and N; then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is known as the pullback (by φ), and is frequently denoted by φ*. More generally, any covariant tensor field – in particular any differential form – on N may be pulled back to M using φ.When the map φ is a diffeomorphism, then the pullback, together with the pushforward, can be used to transform any tensor field from N to M or vice versa. In particular, if φ is a diffeomorphism between open subsets of Rn and Rn, viewed as a change of coordinates (perhaps between different charts on a manifold M), then the pullback and pushforward describe the transformation properties of covariant and contravariant tensors used in more traditional (coordinate dependent) approaches to the subject.The idea behind the pullback is essentially the notion of precomposition of one function with another. However, by combining this idea in several different contexts, quite elaborate pullback operations can be constructed. This article begins with the simplest operations, then uses them to construct more sophisticated ones. Roughly speaking, the pullback mechanism (using precomposition) turns several constructions in differential geometry into contravariant functors.".
- Pullback_(differential_geometry) wikiPageID "494995".
- Pullback_(differential_geometry) wikiPageLength "12031".
- Pullback_(differential_geometry) wikiPageOutDegree "68".
- Pullback_(differential_geometry) wikiPageRevisionID "659954292".
- Pullback_(differential_geometry) wikiPageWikiLink Category:Differential_geometry.
- Pullback_(differential_geometry) wikiPageWikiLink Category:Tensors.
- Pullback_(differential_geometry) wikiPageWikiLink Change_of_coordinates.
- Pullback_(differential_geometry) wikiPageWikiLink Connection_(vector_bundle).
- Pullback_(differential_geometry) wikiPageWikiLink Coordinate_system.
- Pullback_(differential_geometry) wikiPageWikiLink Cotangent_bundle.
- Pullback_(differential_geometry) wikiPageWikiLink Covariance_and_contravariance_of_vectors.
- Pullback_(differential_geometry) wikiPageWikiLink Covariant_derivative.
- Pullback_(differential_geometry) wikiPageWikiLink Diffeomorphism.
- Pullback_(differential_geometry) wikiPageWikiLink Differentiable_manifold.
- Pullback_(differential_geometry) wikiPageWikiLink Differential_form.
- Pullback_(differential_geometry) wikiPageWikiLink Direct_image_functor.
- Pullback_(differential_geometry) wikiPageWikiLink Direct_image_sheaf.
- Pullback_(differential_geometry) wikiPageWikiLink Dual_space.
- Pullback_(differential_geometry) wikiPageWikiLink Exterior_algebra.
- Pullback_(differential_geometry) wikiPageWikiLink Exterior_bundle.
- Pullback_(differential_geometry) wikiPageWikiLink Exterior_derivative.
- Pullback_(differential_geometry) wikiPageWikiLink Fiber_(mathematics).
- Pullback_(differential_geometry) wikiPageWikiLink Fiber_bundle.
- Pullback_(differential_geometry) wikiPageWikiLink Frame_bundle.
- Pullback_(differential_geometry) wikiPageWikiLink General_linear_group.
- Pullback_(differential_geometry) wikiPageWikiLink Lie_derivative.
- Pullback_(differential_geometry) wikiPageWikiLink Linear_map.
- Pullback_(differential_geometry) wikiPageWikiLink Linear_space.
- Pullback_(differential_geometry) wikiPageWikiLink Manifold.
- Pullback_(differential_geometry) wikiPageWikiLink Mathematics.
- Pullback_(differential_geometry) wikiPageWikiLink Open_set.
- Pullback_(differential_geometry) wikiPageWikiLink Pullback.
- Pullback_(differential_geometry) wikiPageWikiLink Pullback_(category_theory).
- Pullback_(differential_geometry) wikiPageWikiLink Pullback_bundle.
- Pullback_(differential_geometry) wikiPageWikiLink Pushforward_(differential).
- Pullback_(differential_geometry) wikiPageWikiLink Ralph_Abraham.
- Pullback_(differential_geometry) wikiPageWikiLink Section_(fiber_bundle).
- Pullback_(differential_geometry) wikiPageWikiLink Sheaf_(mathematics).
- Pullback_(differential_geometry) wikiPageWikiLink Sheaf_of_smooth_functions.
- Pullback_(differential_geometry) wikiPageWikiLink Smooth_manifold.
- Pullback_(differential_geometry) wikiPageWikiLink Smooth_manifolds.
- Pullback_(differential_geometry) wikiPageWikiLink Smooth_map.
- Pullback_(differential_geometry) wikiPageWikiLink Smoothness.
- Pullback_(differential_geometry) wikiPageWikiLink Tangent_bundle.
- Pullback_(differential_geometry) wikiPageWikiLink Tensor.
- Pullback_(differential_geometry) wikiPageWikiLink Tensor_(intrinsic_definition).
- Pullback_(differential_geometry) wikiPageWikiLink Tensor_field.
- Pullback_(differential_geometry) wikiPageWikiLink Tensor_product.
- Pullback_(differential_geometry) wikiPageWikiLink Tensor_product_of_modules.
- Pullback_(differential_geometry) wikiPageWikiLink Vector_bundle.
- Pullback_(differential_geometry) wikiPageWikiLink Vector_bundle_morphism.
- Pullback_(differential_geometry) wikiPageWikiLink Vector_field.
- Pullback_(differential_geometry) wikiPageWikiLink Vector_space.
- Pullback_(differential_geometry) wikiPageWikiLink Wedge_product.
- Pullback_(differential_geometry) wikiPageWikiLinkText "Pullback (differential geometry)".
- Pullback_(differential_geometry) wikiPageWikiLinkText "Pullback".
- Pullback_(differential_geometry) wikiPageWikiLinkText "Pullbacks in differential geometry".
- Pullback_(differential_geometry) wikiPageWikiLinkText "induced map".
- Pullback_(differential_geometry) wikiPageWikiLinkText "pull back".
- Pullback_(differential_geometry) wikiPageWikiLinkText "pull-back".
- Pullback_(differential_geometry) wikiPageWikiLinkText "pullback (differential geometry)".
- Pullback_(differential_geometry) wikiPageWikiLinkText "pullback connection".
- Pullback_(differential_geometry) wikiPageWikiLinkText "pullback sheaf".
- Pullback_(differential_geometry) wikiPageWikiLinkText "pullback".
- Pullback_(differential_geometry) wikiPageWikiLinkText "pullbacks".
- Pullback_(differential_geometry) wikiPageWikiLinkText "pulled back".
- Pullback_(differential_geometry) wikiPageWikiLinkText "pulls back".
- Pullback_(differential_geometry) hasPhotoCollection Pullback_(differential_geometry).
- Pullback_(differential_geometry) wikiPageUsesTemplate Template:Dablink.
- Pullback_(differential_geometry) subject Category:Differential_geometry.
- Pullback_(differential_geometry) subject Category:Tensors.
- Pullback_(differential_geometry) hypernym Map.
- Pullback_(differential_geometry) type Software.
- Pullback_(differential_geometry) comment "Suppose that φ:M→ N is a smooth map between smooth manifolds M and N; then there is an associated linear map from the space of 1-forms on N (the linear space of sections of the cotangent bundle) to the space of 1-forms on M. This linear map is known as the pullback (by φ), and is frequently denoted by φ*.".
- Pullback_(differential_geometry) label "Pullback (differential geometry)".
- Pullback_(differential_geometry) sameAs Pullback.
- Pullback_(differential_geometry) sameAs Rücktransport.
- Pullback_(differential_geometry) sameAs Aplicación_regrediente.
- Pullback_(differential_geometry) sameAs Pull-back.
- Pullback_(differential_geometry) sameAs 당김.
- Pullback_(differential_geometry) sameAs m.02h8f8.
- Pullback_(differential_geometry) sameAs Кодифференциал_(дифференциальная_геометрия).
- Pullback_(differential_geometry) sameAs Кодиференціал_(диференціальна_геометрія).
- Pullback_(differential_geometry) sameAs Q978505.
- Pullback_(differential_geometry) sameAs Q978505.
- Pullback_(differential_geometry) sameAs 拉回_(微分几何).
- Pullback_(differential_geometry) wasDerivedFrom Pullback_(differential_geometry)?oldid=659954292.
- Pullback_(differential_geometry) isPrimaryTopicOf Pullback_(differential_geometry).