Calculating Fundamental Forms for a Parametrized Graph

[Lee33]

Let $f(x,y)=(x,y,h(x,y))$ be a parametrization of the graph $T_h$ of $h:\mathbb{R}^2\to \mathbb{R}$. Compute the first fundamental forms for $T_h$ and also compute the second fundamental form.

For the first fundamental form. I got that $f_u = \langle 1, 0, f_u \rangle$ and $f_v \langle 0,1,f_v \rangle$. Then $f_u \dot\ d_u = 1^2 + f_u^2$, $f_u \dot\ f_v = f_uf_v$ and $f_v \dot\ f_v = 1^2 + f_v^2$.

How can I complete this?

 

[dirk_mec1]

Use PF standard homework format!