- #1
foxjwill
- 354
- 0
1. Homework Statement
Is the gaussian curvature at a point on the surface
[tex]
\frac{1}{(x^2+y^2+1)^2}?[/tex]
2. 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]
3. The Attempt at a Solution
I basically plugged stuff into the above equations. I'm not sure if they're all correct.
Is the gaussian curvature at a point on the surface
[tex]
\frac{1}{(x^2+y^2+1)^2}?[/tex]
2. 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]
3. The Attempt at a Solution
I basically plugged stuff into the above equations. I'm not sure if they're all correct.