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In Boothby's "An introduction to Differentiable Manifolds ...", page 69, Remark 4.2:

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I am unable to discover two cubes of same side length, as asked for. I shall feel very thankful if anyone give some hint.

Zev Chonoles
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R K Sinha
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    Can you please explain your question a little? I am having difficulty understanding your question :( – MBM Mar 29 '13 at 10:42

1 Answers1

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You are not actually required to describe such cubes. What the remark tells you is that, up to composition by some diffeomorphism, you may assume that $\phi(U)$ and $\psi(V)$ are cubes of the same side length. This gives you a way to locally visualise the image of $N$ in $M$.

A.P.
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