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Math Help - push forward

  1. #1
    Member Mauritzvdworm's Avatar
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    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)
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  2. #2
    Senior Member
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    Uh, just insert the definitions, remembering perhaps that \gamma'(t)(f) = {\mathrm{d}f(\gamma(t))\over \mathrm{d}t}\Big|_{t=t}.
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  3. #3
    Member Mauritzvdworm's Avatar
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    thank you, I did figure it out. Forgot about that definition
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