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Geometric Meaning of Isoparametric Hypersurfaces in a Real Space Form

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Published:2000-03-01
Printed: Mar 2000
• Makoto Kimura
• Sadahiro Maeda
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Abstract

We shall provide a characterization of all isoparametric hypersurfaces $M$'s in a real space form $\tilde{M}(c)$ by observing the extrinsic Wshape of geodesics of $M$ in the ambient manifold $\tilde{M}(c)$.
 MSC Classifications: 53C35 - Symmetric spaces [See also 32M15, 57T15] 53C20 - Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53C22 - Geodesics [See also 58E10]

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