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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The symmetry group of a curve preserves a plane
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by Robert Gulliver and Frank Morgan
Proc. Amer. Math. Soc. 84 (1982), 408-411
DOI: https://doi.org/10.1090/S0002-9939-1982-0640242-2
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Abstract:

It is shown that the symmetries of a closed curve without self-intersections in euclidean or hyperbolic $n$-space have an invariant plane in common. This allows a complete characterization of the symmetry group.
References
  • Henry C. Wente, The Plateau problem for symmetric surfaces, Arch. Rational Mech. Anal. 60 (1975/76), no. 2, 149–169. MR 420448, DOI 10.1007/BF00250677
    • Claude Chevalley, Theory of Lie groups, Vol. I, Princeton Univ. Press, Princeton, NJ., 1946.
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Bibliographic Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 84 (1982), 408-411
  • MSC: Primary 53A04; Secondary 57R99
  • DOI: https://doi.org/10.1090/S0002-9939-1982-0640242-2
  • MathSciNet review: 640242