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Geometric Meaning of Isoparametric Hypersurfaces in a Real Space Form

Published online by Cambridge University Press:  20 November 2018

Makoto Kimura  and
Sadahiro Maeda
Makoto Kimura
Affiliation:
Department of Mathematics Faculty of Education Ibaraki University Bunkyo, Mito, Ibaraki, 310-0056 Japan, email: [email protected]
Sadahiro Maeda
Affiliation:
Department of Mathematics Faculty of Education Ibaraki University Bunkyo, Mito, Ibaraki, 310-0056 Japan, email: [email protected]
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Abstract

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We shall provide a characterization of all isoparametric hypersurfaces ${M}'s$ in a real space form $\tilde{M}\left( c \right)$ by observing the extrinsic shape of geodesics of $M$ in the ambient manifold $\tilde{M}\left( c \right)$.

Keywords

53C3553C2053C22
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 1 , 01 March 2000 , pp. 74 - 78
Copyright
Copyright © Canadian Mathematical Society 2000

References

[1] Cecil, T. E. and Ryan, P. J., Tight and Taut immersions of manifolds. Res. Notes Math. 107, 1985.Google Scholar
[2] Comtet, A., On the Landau levels on the hyperbolic plane. Ann. Physics 173 (1987), 185–209.Google Scholar
[3] Yau, S. T., Open problems in geometry. Proc. Sympos. Pure Math. 54(1993), Part I, 1–28.Google Scholar