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Proceedings of the American Mathematical Society

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



Surfaces with orthogonal families of circles

Author: Thomas Ivey
Journal: Proc. Amer. Math. Soc. 123 (1995), 865-872
MSC: Primary 53A05; Secondary 58A15
MathSciNet review: 1246529
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Abstract: The lines of curvature on a cyclide of Dupin are circular arcs. A surface which carries two orthogonal families of circular arcs must arise as an integral surface of an overdetermined exterior differential system. We show that the only solutions of this system are the cyclides of Dupin.

References [Enhancements On Off] (What's this?)

  • [EDS] R. L. Bryant, S.-S. Chern, R. B. Gardner, H. Goldschmidt, and P. A. Griffiths, Exterior differential systems, Math. Sci. Res. Inst. Publ., Springer-Verlag, New York, 1990. MR 1083148 (92h:58007)
  • [P] U. Pinkall, Cyclides of Dupin, Mathematical Models From the Collections of Universities and Museums, Vol. 2 (Commentary) (G. Fischer, ed.), Vieweg, 1986, pp. 28-30. MR 851009 (88c:00001)

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Keywords: Dupin cyclides, exterior differential systems
Article copyright: © Copyright 1995 American Mathematical Society

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