Classification of separable surfaces with constant Gaussian curvature

2019/12/17 by Hasanis, Thomas, López, Rafael
#Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A10 #Secondary 53C42

paper · doi:10.48550/arxiv.1912.07870

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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