**differential geometry - An equiareal map that is not a**
https://math.stackexchange.com/questions/1594503/an-equiareal-map-that-is-not-a-local-isometry

Dec 31, 2015 · An equiareal map that is not a local isometry. Could you give an example of an equiareal map that is not a local isometry? A local diffeomorphism f: S 1 → S 2 is a local isometry if and only if, for any surface patch σ 1 of S 1, the patches σ 1 and f ∘ σ 1 of S 1 and S 2, respectively, have the same first fundamental form.

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