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I am stuck on this question from a tutorial sheet I am going through.

Compute the mean and Gaussian curvature of a surface in $\mathbb{R}^3$ that is given by

$z=f(x)+g(y)$

for some good functions $f(x)$ and $g(y)$.

I tried calculating the first and second fundamental forms to then find $\kappa=\dfrac{det II}{det I}$ but it seems long and I feel like there should be an easier way. Also that doesn't tell me the mean curvature.

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    It is a slightly tedious calculation, yes. The mean curvature is the trace of the 2nd fundamental form.2012-04-22
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    @Tomas The mean curvature is the trace of the Weingarten map, to be more precise2012-04-22
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    @YuriVyatkin yes, you are right.2012-04-22

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