Hostname: page-component-7479d7b7d-q6k6v Total loading time: 0 Render date: 2024-07-12T22:30:24.992Z Has data issue: false hasContentIssue false
  • English
  • Français

Isoparametric functions and submanifolds

Published online by Cambridge University Press:  18 May 2009

S. M. B. Kashani
S. M. B. Kashani
Affiliation:
Mathematics DepartmentShirf University of TechnolohyP.O. Box 11365–9415Tehran, Iran
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The theory of isoparametric functions and a family of isoparametric hypersurfaces began essentially with E. Cartan in 1930's. He defined a real valued function V defined on a Riemannian space form to be isoparametric if ∥grad υ∥2=TV and ΔV = SV for some real valued functions S, T. Then a family of hypersurfaces Mt, is called isoparametric if Mt,=V-1 (t) where t is a regular value of V.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 2 , May 1993 , pp. 145 - 152
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

REFERENCES

1.Carter, S. and West, A., Isoparametric systems and transnormality. Proc. London Math. Soc. (3), 51 (1985), 520–542.CrossRefGoogle Scholar
2.Hahn, J., Isoparametric hypersurfaces in the pseudo Riemannian space forms. Math. Z. 187 (1984), 195–208.CrossRefGoogle Scholar
3.Kashani, S. M. B., Isoparametric submanifolds in pseudo Riemannian spaces. Thesis, Leeds University, 1988.Google Scholar
4.Nomizu, K., Elie Cartan's work on isoparametric families of hypersurfaces, Proc. of Symposia in Pure Math. (AMS) 27 (1975), 191–200.CrossRefGoogle Scholar
5.Terng, C. L., Isoparametric submanifolds and their Coxeter groups. J. Diff. Geom. 21 (1985), 79–107.Google Scholar