- #1
Lee33
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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?
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?