They could give me some suggestions on how to use the data on the derivative, in:
If $f:\mathbb{R}^{m} \rightarrow \mathbb{R}^{m}$ class is $C^{1}$ such that $\Vert f^{\prime}(x)v\Vert =\Vert v\Vert$, for all $v \in \mathbb{R}^{m}$. then $f$ is isometry.
thank you very much