Journal of Geometry

, 110:20 | Cite as

Translation surfaces with non-zero constant mean curvature in Euclidean space

  • Thomas HasanisEmail author


We prove that the only surface in 3-dimensional Euclidean space \({\mathbb {R}}^3\) with constant and non-zero mean curvature H, constructed by the sum of a planar curve and a space curve, is the circular cylinder of radius \(\frac{1}{2|H|}\).


Translation surface constant mean curvature circular cylinder 

Mathematics Subject Classification

53A10 53C45 



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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IoanninaIoanninaGreece

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