# Gaussian Curvature

## Homework Statement

Is the gaussian curvature at a point on the surface $$g(x,y)=xy$$
$$\frac{1}{(x^2+y^2+1)^2}?$$​

## Homework Equations

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

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

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

## The Attempt at a Solution

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