Classification of separable surfaces with constant Gaussian curvature

Thomas Hasanis; Rafael López

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arXiv · 1912.07870

Classification of separable surfaces with constant Gaussian curvature

Thomas Hasanis·Rafael López

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Abstract

We classify all surfaces with constant Gaussian curvature $K$ in Euclidean $3$-space that can be expressed as an implicit equation of type $f(x)+g(y)+h(z)=0$, where $f$, $g$ and $h$ are real functions of one variable. If $K=0$, we prove that the surface is a surface of revolution, a cylindrical surface or a conical surface, obtaining explicit parametrizations of such surfaces. If $K\not=0$, we prove that the surface is a surface of revolution.

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Thomas Hasanis, Rafael López. 2019-12-17. Classification of separable surfaces with constant Gaussian curvature. https://arxiv.org/abs/1912.07870

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