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Principal curvatures of isoparametric hypersurfaces in |
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| Authors: | Liang Xiao |
| Affiliation: | Department of Mathematics, Graduate School, University of Science and Technology of China (Beijing), P.O. Box 3908, Beijing 100039, P.R.China |
| Abstract: | Let  be an isoparametric hypersurface in  , and  the inverse image of  under the Hopf map. By using the relationship between the eigenvalues of the shape operators of  and  , we prove that  is homogeneous if and only if either  or  is constant, where  is the number of distinct principal curvatures of  and  is the number of non-horizontal eigenspaces of the shape operator on  . |
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