# push forward

• June 7th 2010, 03:21 AM
Mauritzvdworm
push forward
show that $(\phi\circ\gamma)^{\prime}(t)=\phi_{*}(\gamma^{\pr ime}(t))$
where if $v\in T_pM$ is a tangent vector and $\phi:M\rightarrow N$ is a smooth function and we define
$(\phi_{*}v)(f)=v(f\circ\phi)$
$\gamma$ is a curve on $M$
$f:N\rightarrow \mathbb{R}$
(Pushing forward)
• June 7th 2010, 02:53 PM
Uh, just insert the definitions, remembering perhaps that $\gamma'(t)(f) = {\mathrm{d}f(\gamma(t))\over \mathrm{d}t}\Big|_{t=t}$.