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

[foxjwill]

1. Homework Statement
Is the gaussian curvature at a point on the surface
$$\frac{1}{(x^2+y^2+1)^2}?$$

2. Homework 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.

 

[HallsofIvy]

1. Homework Statement
Is the gaussian curvature at a point on the surface
$$\frac{1}{(x^2+y^2+1)^2}?$$

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?
$$z= \frac{1}{(x^2+y^2+1)^2}?$$?

2. Homework 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.