A characteristic property of Delaunay surfaces
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- by Thomas Hasanis and Rafael López PDF
- Proc. Amer. Math. Soc. 148 (2020), 5291-5298 Request permission
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.References
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Additional Information
- Thomas Hasanis
- Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
- MR Author ID: 82090
- Email: thasanis@uoi.gr
- Rafael López
- Affiliation: Departamento de Geometría y Topología, Universidad de Granada, 18071 Granada, Spain
- ORCID: 0000-0003-3108-7009
- Email: rcamino@ugr.es
- 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
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 5291-5298
- MSC (2010): Primary 53A10; Secondary 53C42
- DOI: https://doi.org/10.1090/proc/15200
- MathSciNet review: 4163841