SURFACES WITH ORTHOGONAL FAMILIES OF CIRCLES

Authors
IVEY T
Citation
T. Ivey, SURFACES WITH ORTHOGONAL FAMILIES OF CIRCLES, Proceedings of the American Mathematical Society, 123(3), 1995, pp. 865-872
Citations number
2
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
123
Issue
3
Year of publication
1995
Pages
865 - 872
Database
ISI
SICI code
0002-9939(1995)123:3<865:SWOFOC>2.0.ZU;2-S
Abstract
The lines of curvature on a cyclide of Dupin are circular arcs. A surf ace which carries two orthogonal families of circular arcs must arise as an integral surface of an overdetermined exterior differential syst em. We show that the only solutions of this system are the cyclides of Dupin.