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A characteristic property of Delaunay surfaces

Authors: Thomas Hasanis and Rafael López
Journal: Proc. Amer. Math. Soc. 148 (2020), 5291-5298
MSC (2010): Primary 53A10; Secondary 53C42
Published electronically: September 4, 2020
MathSciNet review: 4163841
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that Delaunay surfaces, besides the plane and the cate- noid, are the only surfaces in Euclidean space with nonzero constant mean curvature that can be expressed by an implicit equation of type $f(x)+g(y)+h(z)=0$, where $f$, $g$ and $h$ are smooth real functions of one variable.

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Additional Information

Thomas Hasanis
Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
MR Author ID: 82090

Rafael López
Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
ORCID: 0000-0003-3108-7009

Keywords: Mean curvature, separable surface, Delaunay surface
Received by editor(s): December 9, 2019
Received by editor(s) in revised form: February 22, 2020
Published electronically: September 4, 2020
Additional Notes: The second author was partially supported by the grant no. MTM2017-89677-P, MINECO/AEI/FEDER, UE
Communicated by: Jiaping Wang
Article copyright: © Copyright 2020 American Mathematical Society