Classification of separable surfaces with constant Gaussian curvature

Thomas Hasanis; Rafael López

Classification of separable surfaces with constant Gaussian curvature

Differential Geometry 2019-12-18 v1

Authors: Thomas Hasanis , Rafael López

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.

Keywords

surfaces with constant gaussian curvature euclidean 3-space implicit equation separable surfaces surface of revolution classification

Cite

@article{arxiv.1912.07870,
  title  = {Classification of separable surfaces with constant Gaussian curvature},
  author = {Thomas Hasanis and Rafael López},
  journal= {arXiv preprint arXiv:1912.07870},
  year   = {2019}
}

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