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Journal of Geometry

, 110:20 | Cite as

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

  • Thomas HasanisEmail author
Article
  • 41 Downloads

Abstract

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 \(\frac{1}{2|H|}\).

Keywords

Translation surface constant mean curvature circular cylinder 

Mathematics Subject Classification

53A10 53C45 

Notes

References

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    Liu, H.: Translation surfaces with constant mean curvature in 3-dimensional spaces. J. Geom. 64, 141–149 (1999)MathSciNetCrossRefGoogle Scholar
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    López, R., Perdomo, O.: Minimal translation surfaces in Euclidean space. J. Geom. Anal. 27, 2926–2937 (2017)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IoanninaIoanninaGreece

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