Gaussian Curvature

  • Thread starter foxjwill
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Homework Statement


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]​


Homework 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]


The Attempt at a Solution



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

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