Deformations of Dupin hypersurfaces
HTML articles powered by AMS MathViewer
- by Ulrich Pinkall and Gudlaugur Thorbergsson PDF
- Proc. Amer. Math. Soc. 107 (1989), 1037-1043 Request permission
Abstract:
Examples are given of compact proper-Dupin hypersurfaces that are not Lie equivalent to an isoparametric hypersurface.References
- Thomas E. Cecil and Shiing Shen Chern, Tautness and Lie sphere geometry, Math. Ann. 278 (1987), no. 1-4, 381–399. MR 909233, DOI 10.1007/BF01458076
- T. E. Cecil and P. J. Ryan, Tight and taut immersions of manifolds, Research Notes in Mathematics, vol. 107, Pitman (Advanced Publishing Program), Boston, MA, 1985. MR 781126
- Dirk Ferus, Hermann Karcher, and Hans Friedrich Münzner, Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z. 177 (1981), no. 4, 479–502 (German). MR 624227, DOI 10.1007/BF01219082
- Karsten Grove and Stephen Halperin, Dupin hypersurfaces, group actions and the double mapping cylinder, J. Differential Geom. 26 (1987), no. 3, 429–459. MR 910016
- Wu-yi Hsiang and H. Blaine Lawson Jr., Minimal submanifolds of low cohomogeneity, J. Differential Geometry 5 (1971), 1–38. MR 298593
- Dale Husemoller, Fibre bundles, McGraw-Hill Book Co., New York-London-Sydney, 1966. MR 0229247
- Reiko Miyaoka, Compact Dupin hypersurfaces with three principal curvatures, Math. Z. 187 (1984), no. 4, 433–452. MR 760045, DOI 10.1007/BF01174180
- Reiko Miyaoka, Dupin hypersurfaces and a Lie invariant, Kodai Math. J. 12 (1989), no. 2, 228–256. MR 1002665, DOI 10.2996/kmj/1138039036
- Reiko Miyaoka and Tetsuya Ozawa, Construction of taut embeddings and Cecil-Ryan conjecture, Geometry of manifolds (Matsumoto, 1988) Perspect. Math., vol. 8, Academic Press, Boston, MA, 1989, pp. 181–189. MR 1040525 H.-F. Münzner, Isoparametrische Hyperflächen in Sphären I, Math. Ann. 251 (1980), 57-71; II, 256 (1981), 215-232.
- U. Pinkall, Dupin hypersurfaces, Math. Ann. 270 (1985), no. 3, 427–440. MR 774368, DOI 10.1007/BF01473438
- Ryoichi Takagi and Tsunero Takahashi, On the principal curvatures of homogeneous hypersurfaces in a sphere, Differential geometry (in honor of Kentaro Yano), Kinokuniya, Tokyo, 1972, pp. 469–481. MR 0334094
- Gudlaugur Thorbergsson, Dupin hypersurfaces, Bull. London Math. Soc. 15 (1983), no. 5, 493–498. MR 705529, DOI 10.1112/blms/15.5.493
- Qi Ming Wang, On the topology of Clifford isoparametric hypersurfaces, J. Differential Geom. 27 (1988), no. 1, 55–66. MR 918456
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 1037-1043
- MSC: Primary 53C40; Secondary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-1989-0975655-9
- MathSciNet review: 975655