= Pushforward of a contravariant tensor
{title2=$\phi_*T=(d\phi)^{\otimes r}T$}
The <pushforward of a contravariant tensor> applies the <differential of a smooth map> to each vector factor of a type $(r,0)$ tensor. It is defined pointwise at a specified source point. A field generally gives a field along the map, not necessarily a unique tensor field on the image when several points have the same image. A <diffeomorphism> allows the usual transport of arbitrary mixed tensors through its inverse as well.
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