Translation surfaces in Euclidean space with constant Gaussian curvature

2018/09/08 by Thomas Hasanis, Hasanis, Thomas, Rafael López +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1809.02758

openalex publication_date 2018/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the only surfaces in 3-dimensional Euclidean space \R³ with constant Gaussian curvature K and constructed by the sum of two space curves are cylindrical surfaces, in particular, K=0.

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• Maximal translation surfaces in Lorentz-Minkowski space

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