I've got the following surface $M=\bigl\{(x,y,z) \mid e^z=\frac{\cos x}{\cos y}\bigr\}\subset \mathbb{R}^3$ where $x,y \in \bigl(-\frac{\pi}{2},\frac{\pi}{2}\bigr)$ and want to calculate the mean curvature of it.
To do this I used the parametrisation $X(u,v)=(u,v,\ln(\frac{\cos u}{\cos v}))$ but this leads to to a complete mess when using the well known formula
$\dfrac{1}{2}\dfrac{eG-2fF+gE}{EG-F^2}$
where $E,F,G$ is from the first and $e,f,g$ is from the second fundamental forms.
Someone know how to do this so it doesn't go off the handle?
I have Gauss map given by $$N(X(u,v))=(\tan u,-\tan v, 1) \dfrac{1}{\sqrt{\dfrac{-\sin^2u}{\cos^2u}+\dfrac{-\sin^2v}{\cos^2v}+1}}.$$
Best Answer
Scherk Surface
How the coefficients of FFF and SFF are calculated is mentioned.