Skip to main content

Dupin submanifolds in lie sphere geometry

  • Conference paper
  • First Online:
Differential Geometry and Topology

Part of the book series: Lecture Notes in Mathematics ((2803,volume 1369))

The first author was supported by NSF Grant No. DMS 87-06015, the second author by NSF Grant No. DMS 87-01609.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. W. Blaschke, Vorlesungen über Differentialgeometrie, Vol. 3, Springer, Berlin, 1929.

    Google Scholar 

  2. T. Cecil and S.S. Chern, Tautness and Lie sphere geometry, Math. Ann. 278 (1987), 381–399.

    Article  MathSciNet  MATH  Google Scholar 

  3. T. Cecil and P. Ryan, Tight and taut immersions of manifolds, Res. Notes Math. 107, Pitman, London, 1985.

    MATH  Google Scholar 

  4. L. Eisenhart, A treatise on the differential geometry of curves and surfaces, Ginn, Boston, 1909.

    MATH  Google Scholar 

  5. K. Grove and S. Halperin, Dupin hypersurfaces, group actions and the double mappings cylinder, J. Differential Geometry 26 (1987), 429–459.

    MathSciNet  MATH  Google Scholar 

  6. E.P. Lane, A treatise on projective differential geometry, U. Chicago Press, Chicago, 1942.

    MATH  Google Scholar 

  7. S. Lie and G. Scheffers, Geometrie der Berührungstransformationen, Teubner, Leipzig, 1896.

    Google Scholar 

  8. R. Miyaoka, Compact Dupin hypersurfaces with three principal curvatures, Math. Z. 187 (1984), 433–452.

    Article  MathSciNet  MATH  Google Scholar 

  9. ___, Dupin hypersurfaces with four principal curvatures, Preprint, Tokyo Institute of Technology.

    Google Scholar 

  10. ___, Dupin hypersurfaces with six principal curvatures, Preprint, Tokyo Institute of Technology.

    Google Scholar 

  11. H.F. Münzner, Isoparametrische Hyperflächen in Sphären, I and II, Math. Ann. 251 (1980), 57–71 and 256 (1981), 215–232.

    Article  MathSciNet  MATH  Google Scholar 

  12. K. Nomizu, Characteristic roots and vectors of a differentiable family of symmetric matrices, Lin. and Multilin. Alg. 2 (1973), 159–162.

    Article  MathSciNet  MATH  Google Scholar 

  13. U. Pinkall, Dupin'sche Hyperflächen, Dissertation, Univ. Freiburg, 1981.

    Google Scholar 

  14. ___, Dupin'sche Hyperflächen in E 4, Manuscr. Math 51 (1985), 89–119.

    Article  MathSciNet  MATH  Google Scholar 

  15. ___, Dupin hypersurfaces, Math. Ann. 270 (1985), 427–440.

    Article  MathSciNet  MATH  Google Scholar 

  16. D. Singley, Smoothness theorems for the principal curvatures and principal vectors of a hypersurface, Rocky Mountain J. Math., 5 (1975), 135–144.

    Article  MathSciNet  MATH  Google Scholar 

  17. G. Thorbergsson, Dupin hypersurfaces, Bull. Lond. Math. Soc. 15 (1983), 493–498.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Boju Jiang Chia-Kuei Peng Zixin Hou

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Cecil, T.E., Chern, SS. (1989). Dupin submanifolds in lie sphere geometry. In: Jiang, B., Peng, CK., Hou, Z. (eds) Differential Geometry and Topology. Lecture Notes in Mathematics, vol 1369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087525

Download citation

  • DOI: https://doi.org/10.1007/BFb0087525

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51037-6

  • Online ISBN: 978-3-540-46137-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics