# Gaussian Curvature

1. May 22, 2008

### foxjwill

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

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

Gaussian Curvature = $$|S(\textbf{x})|$$

$$\hat{\textbf{n}}=\frac{\nabla g}{\|\nabla g\|}$$

3. The attempt at a solution

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