Let q and q' be sufficiently close points on C^oo manifold M.(adsbygoogle = window.adsbygoogle || []).push({});

Then is it true that any C^oo curve c:[a,b]-->M where c(a)=q, c(q)=q' can be represented as c(t)=exp[tex]_{q}[/tex](u(t)v(t)) where u:[a,b]-->R,v:[a,b]-->TM[tex]_{q}[/tex] and ||v||=1?

My question comes from Chapter 9 corollary 16 and 17 of Spivak vol1.

In the proof of corollary 17 I think he assumes this fact.

Thanks.

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# Exponential map

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