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 September 26th, 2007, 03:24 PM #1 Newbie   Joined: Sep 2007 Posts: 1 Thanks: 0 Isometric surfaces - differential geometry Hi everybody! I'm writing here because I need to answer to this problem: Let f:R^2--->R^3, (u,v)|-->(u,v,3u^3-4v^2) be a parametrization of the Surface S and let g:R^2--->R^3, (u,v)|-->(u,v,3u^3-4(u+v)^2) be a parametrization of the surface S'. Tell if S and S' are (locally) isometric. I find really difficult to understand what are 2 isometric surfaces! I mean, I know about cilinder and plane, etc... But I really can't understand how to prove that two general surfaces are isometric! I tried to use the Gauss Egregium Theorem to prove that are not isometric, but in this case it didn't work because the K are equal for both surfaces! I even thought about finding a re-parametrization for g : phi:R^2-->R^2, (u,v)|-->(u,v-u) but is this an isometry? Or else, how can I find an isometry? How can I create such a map? I really hope that someone can help me because this will be part of my oral test.... Thank You so much

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