Communications in Analysis and Geometry

Volume 29 (2021)

Number 6

Translation surfaces in Euclidean space with constant Gaussian curvature

Pages: 1415 – 1447

DOI: https://dx.doi.org/10.4310/CAG.2021.v29.n6.a4

Authors

Thomas Hasanis (Department of Mathematics, University of Ioannina, Greece)

Rafael López (Departamento de Geometría y Topología, Instituto de Matemáticas, Universidad de Granada, Spain)

Abstract

We prove that the only surfaces in $3$-dimensional Euclidean space $\mathbb{R}^3$ 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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This work was partially supported by the grant no. MTM2017-89677-P, MINECO/AEI/FEDER, UE.

Received 26 January 2018

Accepted 31 January 2019

Published 11 January 2022