Ok, in general, I know that if the coefficients of the First Fundamental Form agree for two surfaces parameterized by X and Y, the the map X(Y^-1) is an isometry, or the two surfaces are isometric.(adsbygoogle = window.adsbygoogle || []).push({});

I also know that if two parameterizations don't have the same coefficients, this does not imply that the two surfaces are not isometric.

So i have two parameterizationsthat have different coefficients of the FFF (first fundamental form) but have the same Gaussian curvature. I need to prove that the two surfaces are not isometric. (ie i need to prove that the converse of Gauss's Great Theorem is false).

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# Homework Help: Differential Geometry general question

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