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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) wikiPageRevisionID "585059488".
- Pullback_(differential_geometry) hasPhotoCollection Pullback_(differential_geometry).
- Pullback_(differential_geometry) subject Category:Differential_geometry.
- Pullback_(differential_geometry) subject Category:Tensors.
- Pullback_(differential_geometry) type Abstraction100002137.
- Pullback_(differential_geometry) type Cognition100023271.
- Pullback_(differential_geometry) type Concept105835747.
- Pullback_(differential_geometry) type Content105809192.
- Pullback_(differential_geometry) type Idea105833840.
- Pullback_(differential_geometry) type PsychologicalFeature100023100.
- Pullback_(differential_geometry) type Quantity105855125.
- Pullback_(differential_geometry) type Tensor105864481.
- Pullback_(differential_geometry) type Tensors.
- Pullback_(differential_geometry) type Variable105857459.
- 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 "Aplicación regrediente".
- Pullback_(differential_geometry) label "Pull-back".
- Pullback_(differential_geometry) label "Pullback (differential geometry)".
- Pullback_(differential_geometry) label "Rücktransport".
- Pullback_(differential_geometry) label "Кодифференциал (дифференциальная геометрия)".
- Pullback_(differential_geometry) label "拉回 (微分几何)".
- 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 Q978505.
- Pullback_(differential_geometry) sameAs Q978505.
- Pullback_(differential_geometry) sameAs Pullback_(differential_geometry).
- Pullback_(differential_geometry) wasDerivedFrom Pullback_(differential_geometry)?oldid=585059488.
- Pullback_(differential_geometry) isPrimaryTopicOf Pullback_(differential_geometry).