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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The symmetry group of a curve preserves a plane


Authors: Robert Gulliver and Frank Morgan
Journal: Proc. Amer. Math. Soc. 84 (1982), 408-411
MSC: Primary 53A04; Secondary 57R99
MathSciNet review: 640242
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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 [Enhancements On Off] (What's this?)

  • [1] Henry C. Wente, The Plateau problem for symmetric surfaces, Arch. Rational Mech. Anal. 60 (1975/76), no. 2, 149–169. MR 0420448 (54 #8462)
  • [2] Claude Chevalley, Theory of Lie groups, Vol. I, Princeton Univ. Press, Princeton, NJ., 1946.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0640242-2
PII: S 0002-9939(1982)0640242-2
Article copyright: © Copyright 1982 American Mathematical Society