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Deformations of Dupin hypersurfaces

Authors: Ulrich Pinkall and Gudlaugur Thorbergsson
Journal: Proc. Amer. Math. Soc. 107 (1989), 1037-1043
MSC: Primary 53C40; Secondary 53C20
MathSciNet review: 975655
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Abstract: Examples are given of compact proper-Dupin hypersurfaces that are not Lie equivalent to an isoparametric hypersurface.

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  • [CC] T. E. Cecil and S.-S. Chern, Tautness and Lie sphere geometry, Math. Ann. 278 (1987), 381-399. MR 909233 (89e:53084)
  • [CR] T. E. Cecil and P. J. Ryan, Tight and taut immersions of manifolds, Res. Notes Math. 107, Ptiman, Boston, London, Melbourne 1985. MR 781126 (87b:53089)
  • [FKM] D. Ferus, H. Karcher and H.-F. Münzner, Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z. 177 (1981), 479-502. MR 624227 (83k:53075)
  • [GH] K. Grove and S. Halperin, Dupin hypersurfaces, group actions and the double mapping cylinder, J. Differential Geom. 26 (1987), 429-457. MR 910016 (89h:53113)
  • [HL] W.-Y. Hsiangand H. B. Lawson, Minimal submanifolds of low cohomogeneity, J. Differential Geometry 5 (1971), 1-38. MR 0298593 (45:7645)
  • [Hu] D. Husemoller, Fibre bundles, McGraw-Hill, New York, 1966. MR 0229247 (37:4821)
  • [Mi1] R. Miyaoka, Compact Dupin hypersurfaces with three principal curvatures, Math. Z. 187 (1984), 433-452. MR 760045 (85h:53041)
  • [Mi2] -, Dupin hypersurfaces and a Lie invariant, (to appear in Kodai Math. J.). MR 1002665 (90i:53083)
  • [MO] R. Miyaoka and T. Ozawa, Construction of taut embeddings and Cecil-Ryan conjecture, preprint, Tokyo Institute of Technology and Nagoya University 1988. MR 1040525 (92f:53071)
  • [Mü] H.-F. Münzner, Isoparametrische Hyperflächen in Sphären I, Math. Ann. 251 (1980), 57-71; II, 256 (1981), 215-232.
  • [Pi] U. Pinkall, Dupin hypersurfaces, Math. Ann. 270 (1985), 427-440. MR 774368 (86e:53044)
  • [TT] R. Takagi and T. Takahashi, On the principal curvatures of homogeneous hypersurfaces in a sphere, in Differential Geometry in Honor of K. Yano, Kinokuniya, Tokyo 1972, 469-481. MR 0334094 (48:12413)
  • [Th] G. Thorbergsson, Dupin hypersurfaces, Bull. London Math. Soc. 15 (1983), 493-498. MR 705529 (85b:53066)
  • [Wa] Q.-M. Wang, On the topology of Clifford isoparametric hypersurfaces, J. Differential Geometry 27 (1988), 55-66. MR 918456 (89e:53093)

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Article copyright: © Copyright 1989 American Mathematical Society

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