push forward

**Mauritzvdworm** · June 7th 2010, 03:21 AM

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)

**maddas** · June 7th 2010, 02:53 PM

Uh, just insert the definitions, remembering perhaps that $\gamma'(t)(f) = {\mathrm{d}f(\gamma(t))\over \mathrm{d}t}\Big|_{t=t}$ .

**Mauritzvdworm** · June 7th 2010, 09:15 PM

thank you, I did figure it out. Forgot about that definition

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