Tohoku Mathematical Journal

An algebraic approach to isoparametric hypersurfaces in spheres, I

Josef Dorfmeister and Erhard Neher

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 35, Number 2 (1983), 187-224.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178229050

Digital Object Identifier
doi:10.2748/tmj/1178229050

Mathematical Reviews number (MathSciNet)
MR0699927

Zentralblatt MATH identifier
0507.53038

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]

Citation

Dorfmeister, Josef; Neher, Erhard. An algebraic approach to isoparametric hypersurfaces in spheres, I. Tohoku Math. J. (2) 35 (1983), no. 2, 187--224. doi:10.2748/tmj/1178229050. https://projecteuclid.org/euclid.tmj/1178229050


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References

  • [1] E. CARTAN, Sur des families remarquables d'hypersurfaces isoparametriques dans les espaces spheriques, Ann. Mat. Pura Appl. 17 (1938), 177-191.
  • [2] J. DORFMEISTER AND E. NEHER, An algebraic approach to isoparametric hypersurface in spheres II, this volume, 225-247.
  • [3] J. DORFMEISTER AND E. NEHER, Isoparametric triple systems of algebra type, to appea in Osaka J. Math.
  • [4] J. DORFMEISTER AND E. NEHER, Isoparametric triple systems of FKM-type, I, II, III, t appear.
  • [5] D. FERUS, Notes on isoparametric hypersurfaces, Universidade estadual de campinas, Brasil 1980.
  • [6] D. FERUS, H. KARCHER AND H. F. MUNZNER, Cliffordalgebren und neue isoparametrisch Hyperflachen, Math. Z. 177 (1981), 479-502.
  • [7] H. F. MUNZNER, Isoparametrische Hyperflachen in Spharen I, Math. Ann. 251 (1980), 57-71.
  • [8] H. F. MUNZNER, Isoparametrische Hyperflachen in Spharen II, Math. Ann. 256 (1981), 215-232.
  • [9] K. NOMIZU, Some results in E. Cartan's theory of isoparametric families of hypersur faces, Bull. Amer. Math. Soc. 79 (1973/4), 1184-1188.
  • [10] H. OZEKI AND M. TAKEUCHI, On some types of isoparametric hypersurfaces in spheres I, Thoku Math. J. 27 (1975), 515-559.
  • [11] H. OZEKI AND M. TAKEUCHI, On some types of isoparametric hypersurfaces in spheres II, Thoku Math. J. 28 (1976), 7-55.
  • [12] R. TAKAGI AND T. TAKAHASHI, On the principal curvatures of homogeneous hypersurface in a sphere, Differential Geometry, in honor of K. Yano, edited by S. Kobayashi, M. Obata and T. Takahashi.

See also

  • Part II: Josef Dorfmeister, Erhard Neher. An algebraic approach to isoparametric hypersurfaces in spheres, II. Tohoku Math. J., Volume 35, Number 2 (1983), pp. 225-247.