|
Affine Dupin Surfaces
Author(s):
Ross
Niebergall;
Patrick
J.
Ryan
Journal:
Trans. Amer. Math. Soc.
348
(1996),
1093-1115.
MSC (1991):
Primary 53A15;
Secondary 53A05, 53B25
MathSciNet review:
1316860
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper we study nondegenerate affine surfaces in  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:
- [C]
- T. E. Cecil, Lie sphere geometry with applications to submanifolds, Universitext, Springer-
Verlag, New York, Berlin, Heidelberg, 1992. MR 94m:53076 - [CR]
- T. E. Cecil and P. J. Ryan, Tight and taut immersions of manifolds, Research Notes in Math., vol. 107, Pitman, Boston, London, Melbourne, 1985. MR 87b:53089
- [K]
- W. Klingenberg, A course in differential geometry, Graduate Texts in Math., vol. 51, Springer-Verlag, New York, Heidelberg, Berlin, 1978. MR 57:13702
- [MR]
- M. A. Magid and P. J. Ryan, Flat affine spheres in
 , Geom. Dedicata 33 (1990), 277--288. MR 91e:53016 - [NR1]
- R. Niebergall and P. J. Ryan, Affine isoparametric hypersurfaces, Math. Z. 217 (1994), 479--485. MR 96a:53015
- [NR2]
- ------, Focal sets in affine geometry, Geometry and Topology of Submanifolds VI, World Scientific, 1994. CMP 95:07
- [N]
- K. Nomizu, Introduction to affine differential geometry, Part I, MPI/88--37, Bonn, 1988.
- [NS]
- K. Nomizu and T. Sasaki, A new model of unimodular-affinely homogeneous surface, Manu-
scripta Math. 73 (1991), 39--44. MR 92h:53014 - [V]
- L. Vrancken, Affine surfaces with constant affine curvatures, Geom. Dedicata 33 (1990), 177--194. MR 91k:53022
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (1991):
53A15,
53A05, 53B25
Retrieve articles in all Journals with
MSC (1991):
53A15,
53A05, 53B25
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:
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.
Copyright of article:
Copyright
1996,
American Mathematical Society
|
