I know this may sounds silly but I am confused(adsbygoogle = window.adsbygoogle || []).push({});

consider this two form for example, by substitution, I get

[tex]\omega = dx \wedge dy = d(rCos\theta)\wedge d(rSin\theta) = r dr \wedge d\theta[/tex]

also consider this smooth map [tex]F(x,y)=(rCos\theta,rSin\theta)[/tex]

then [tex]F^{*}\omega = rdr \wedge d\theta[/tex]

which means that [tex]F^{*}\omega= \omega[/tex]!?, that's just weird.

I am reading John's Lee smooth manifold book. and I saw the substitution writing at the differential form chapter. and the pullback writing at the Covector field chapter.

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# Weird result on forms?

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