Pushforward of a curve
= Pushforward of a curve
{title2=$\phi_*\lambda=\phi\circ\lambda$}
A <pushforward of a curve> composes a parametrized curve in the source with a <smooth map between manifolds>. Its tangent is the image of the original tangent under the <differential of a smooth map>. A constant image curve has zero tangent, so a general smooth map need not preserve regularity of curves.