Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T20:24:37.966Z Has data issue: false hasContentIssue false
  • English
  • Français

Quadratic isoparametric systems in ℝn+mp

Published online by Cambridge University Press:  18 May 2009

S. M. B. Kashani
Rights & Permissions [Opens in a new window]

Abstract

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 notions of isoparametric maps and submanifolds in semi-Riemannian spaces are the generalizations of such notions in Riemannian spaces. The generalizations are different according to the purposes. We take the definitions as in the Riemannian case. Quadratic isoparametric maps and submanifolds are interesting examples which can be studied in detail. In this paper we study what we call quadratic isoparametric systems. In fact we give a classification of such systems of codimension 2. We use three different methods to show that quadratic isoparametric submanifolds of codimension 2 are homogeneous. The classification of quadratic isoparametric systems is done algebraically. By this we have changed the geometric problem of classifying quadratic submanifolds of codimension 2 into the algebraic problem of classifying quadratic isoparametric systems of codimension 2. The classification of such systems with arbitrary codimension is still open.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 35 , Issue 2 , May 1993 , pp. 135 - 143
Copyright
Copyright © Glasgow Mathematical Journal Trust 1993

References

REFERENCES

1.Hahn, J., Isoparametric hypersurfaces in the pseudo-Riemannian space forms, Math. Z. 187 (1984), 195–208.Google Scholar
2.Kashani, S. M. B., Isoparametric submanifolds in pseudo-Riemannian spaces, Thesis, Leeds University, 1988.Google Scholar
3.Magid, M. A., Isometric immersions between indefinite flat spaces with parallel second fundamental forms, Thesis, Brown University, 1978.Google Scholar
4.O'Neill, B., Semi-Riemannian geometry with applications to relativity (Academic Press, New York, 1983).Google Scholar