Geometriae Dedicata

, Volume 42, Issue 3, pp 311–315 | Cite as

Surfaces which contain helical geodesics

  • Michiko Tamura
Article

Abstract

LetM be a complete smooth surface of constant mean curvature in the Euclidean 3-space. If there exists two helical geodesics onM through each point ofM, thenM is either a plane, a sphere, or a circular cylinder.

Keywords

Smooth Surface Circular Cylinder Complete Smooth Surface 

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References

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    Takeuchi, N., ‘A surface which contains planar geodesics’,Geom. Dedicata 27 (1988), 223–225.CrossRefMATHMathSciNetGoogle Scholar
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    Takeuchi, N. and Tamura, M., ‘A surface which contains helical geodesics’,Bull. Tokyo Gakugei Univ. (4)43 (1990), 15–18.MathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Michiko Tamura
    • 1
  1. 1.Department of MathematicsTokyo Gakugei UniversityTokyoJapan

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