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Gaussian Curvature

  1. May 22, 2008 #1
    1. The problem statement, all variables and given/known data
    Is the gaussian curvature at a point on the surface [tex]g(x,y)=xy[/tex]
    [tex]\frac{1}{(x^2+y^2+1)^2}?[/tex]​


    2. Relevant equations
    shape operator:
    [tex]S(\textbf{x})=-D_\textbf{x}\hat{\textbf{n}}=\frac{\partial (n_x, n_y)}{\partial (x,y)}[/tex]​

    Gaussian Curvature = [tex]|S(\textbf{x})|[/tex]

    [tex]\hat{\textbf{n}}=\frac{\nabla g}{\|\nabla g\|}[/tex]


    3. The attempt at a solution

    I basically plugged stuff into the above equations. I'm not sure if they're all correct.
     
  2. jcsd
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