Surfaces with orthogonal families of circles
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- by Thomas Ivey PDF
- Proc. Amer. Math. Soc. 123 (1995), 865-872 Request permission
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
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 865-872
- MSC: Primary 53A05; Secondary 58A15
- DOI: https://doi.org/10.1090/S0002-9939-1995-1246529-6
- MathSciNet review: 1246529