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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Affine Dupin Surfaces


Authors: Ross Niebergall and Patrick J. Ryan
Journal: Trans. Amer. Math. Soc. 348 (1996), 1093-1115
MSC (1991): Primary 53A15; Secondary 53A05, 53B25
MathSciNet review: 1316860
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Abstract: In this paper we study nondegenerate affine surfaces in ${\mathbb R} ^{3}$ whose affine principal curvatures are constant along their lines of curvature. We give a complete local classification of these surfaces assuming that the lines of curvature are planar, and there are no umbilics.


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Additional Information

Ross Niebergall
Affiliation: Department of Mathematics and Computer Science, University of Northern British Columbia, Prince George, BC, Canada V2L 5P2
Email: rossn@unbc.edu

Patrick J. Ryan
Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada, L8S 4K1
Email: pjr@maccs.dcss.mcmaster.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01458-4
PII: S 0002-9947(96)01458-4
Received by editor(s): September 1, 1994
Received by editor(s) in revised form: February 6, 1995
Additional Notes: Research supported by an NSERC Postdoctoral Fellowship and NSERC Operating Grant OGP0002501.
Article copyright: © Copyright 1996 American Mathematical Society