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In this previous question: Transported Metric, I wanted to transport the Euclidean metric $ds^2=dx^2+dy^2$ into the first quadrant of the $(u,v)$-plane, such that for all curves $\gamma$ in the $(x,y)$-plane we have $L_{uv}\bigl(f(\gamma)\bigr)=L_{xy}(\gamma)$.
I used a map $f:\Bbb R^2\to\Bbb R^{...
