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Gaussian Curvature of (x^2+y^2+1)^-2

  1. May 27, 2008 #1
    1. The problem statement, all variables and given/known data
    Is the gaussian curvature at a point on the surface

    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]

    \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
  3. May 27, 2008 #2


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    Staff Emeritus
    Science Advisor

    I have no idea what you mean by this that is an equation, not a surface. It's graph, in the xy-plane is a curve, not a surface. What surface do you mean?
    [tex]z= \frac{1}{(x^2+y^2+1)^2}?[/tex]?

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