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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^34v^2) be a parametrization of the Surface S and let g:R^2>R^3, (u,v)>(u,v,3u^34(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 reparametrization for g : phi:R^2>R^2, (u,v)>(u,vu) 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 

Tags 
differential, geometry, isometric, surfaces 
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