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On a theorem by Hsiang and Yu

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Abstract

In 1841, Delaunay classified surfaces of revolution with constant mean curvature in the Euclidean three space. As a byproduct of his result, one obtains: A surface of revolution has a periodic generating curve if and only if its mean curvature is non-zero. One hundred and forty years after Delaunay’s work, Hsiang and Yu extended this result to higher dimensions, by extending Delaunay’s idea of tracing the locus of a focus by rolling a given conic section along a line. In this paper, we give a new proof of their result using elementary ODE theory to obtain the periodicity of the solutions under consideration.

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References

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Authors and Affiliations

  1. Zentrum Mathematik M 8, TU-Muenchen, Boltzmann Str. 3, 85747, Garching, Germany

    Josef Dorfmeister

  2. Mathematical Institute, Tohoku University, 980-8578, Sendai, Japan

    Katsuei Kenmotsu

Authors
  1. Josef Dorfmeister
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  2. Katsuei Kenmotsu
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Correspondence to Katsuei Kenmotsu.

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Dorfmeister, J., Kenmotsu, K. On a theorem by Hsiang and Yu. Ann Glob Anal Geom 33, 245–252 (2008). https://doi.org/10.1007/s10455-007-9083-7

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  • DOI: https://doi.org/10.1007/s10455-007-9083-7

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