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Classification of separable surfaces with constant Gaussian curvature

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Abstract

We classify all surfaces with constant Gaussian curvature K in Euclidean 3-space that can be expressed by an implicit equation of type \(f(x)+g(y)+h(z)=0\), where f, g and h are real functions of one variable. If \(K=0\), we prove that the surface is a surface of revolution, a cylindrical surface or a conical surface, obtaining explicit parametrizations of such surfaces. If \(K\not =0\), we prove that the surface is a surface of revolution.

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Acknowledgements

Rafael López has been partially supported by the Grant No. MTM2017-89677-P, MINECO/AEI/FEDER, UE.

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Authors and Affiliations

  1. Department of Mathematics, University of Ioannina, 45110, Ioannina, Greece

    Thomas Hasanis

  2. Departamento de Geometría y Topología, Universidad de Granada, 18071, Granada, Spain

    Rafael López

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  1. Thomas Hasanis
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  2. Rafael López
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Correspondence to Rafael López.

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Hasanis, T., López, R. Classification of separable surfaces with constant Gaussian curvature. manuscripta math. 166, 403–417 (2021). https://doi.org/10.1007/s00229-020-01247-6

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  • DOI: https://doi.org/10.1007/s00229-020-01247-6

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