Pullback (differential geometry)

Common card · No. 374675

Let ϕ : M → N {\displaystyle \phi :M\to N} be a smooth map between smooth manifolds M {\displaystyle M} and N {\displaystyle N} . Then there is an associated linear map from the space of 1-forms on N {\displaystyle N} (the linear space of sections of the cotangent bundle) to the space of 1-forms on M {\displaystyle M} . This linear map is known as the pullback (by ϕ {\displaystyle \phi } ), and is frequently denoted by ϕ ∗ {\displaystyle \phi ^{*}} . More generally, any covariant tensor field – in particular any differential form – on N {\displaystyle N} may be...

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