How can I compute the Gaussian curvature of a level set of the form $S =\{(x,y,z)\in\mathbb R^3 : f(x,y,z) = 0\}$? The particular example I'm looking at is $$f(x,y,z) = e^z\cos x - \cos y.$$ I wanted to find a global parametrisation of the surface but I don't think one exists.
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That's true. How does that help? – IAlreadyHaveAKey Nov 06 '16 at 09:51
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I'm sorry I don't see how that makes it any easier to parametrise. – IAlreadyHaveAKey Nov 06 '16 at 13:36
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Perhaps this old question and answer will be of assistance. – Ted Shifrin Nov 06 '16 at 18:47
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use $(x,y)\mapsto(x,y,\ln\frac{\cos y}{\cos x})$ as a Monge's chart – janmarqz Nov 06 '16 at 22:49
