Affine Dupin Surfaces
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- by Ross Niebergall and Patrick J. Ryan
- Trans. Amer. Math. Soc. 348 (1996), 1093-1115
- DOI: https://doi.org/10.1090/S0002-9947-96-01458-4
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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.References
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Bibliographic 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
- 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.
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 1093-1115
- MSC (1991): Primary 53A15; Secondary 53A05, 53B25
- DOI: https://doi.org/10.1090/S0002-9947-96-01458-4
- MathSciNet review: 1316860