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I am currently studying differential geometry. And I would like to know how one shows that two curves are not equivalent.

I know that two curves $c_1: I \rightarrow \mathbb{R^n}$ and $c_2: J \rightarrow \mathbb{R^n}$ are said to be equivalent if there exists function $\phi: I \rightarrow J$ s.t $c_2 = c_1 \circ \phi$

Now, In an exercice, I am asked to show that two curves are not equivalent. i.e: I am supposed to show that there doesn't exist $\phi$ s.t. $c_2 = c_1 \circ \phi$.

I don't know how to do that.

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    Any condition on the curves, for sure... – 2017-02-24
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    Different arclength, curvature, etc.? – 2017-02-24
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    First draw a picture : if they have not the same image, they are not equivalent. If they have the same image and are "smooth enough" ( for instance these curves are immersions) then they are equivalent. – 2017-02-24

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