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.
2026-03-28 11:22:04.1774696924
Gaussian Curvature of a Level surface
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You will find an explicit formula here