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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 | References | Similar Articles | Additional Information

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

PII: S 0002-9939(1982)0640242-2
Article copyright: © Copyright 1982 American Mathematical Society

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