ISOPARAMETRIC HYPERSURFACES IN $\[C{P^n}\]$ WITH CONSTANT PRINCIPAL CURVATURES
Citation：
Li Zhenqi.ISOPARAMETRIC HYPERSURFACES IN $\[C{P^n}\]$ WITH CONSTANT PRINCIPAL CURVATURES[J].Chinese Annals of Mathematics B,1988,9(4):485~493
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Authors：
Li Zhenqi;
Foundation：
Project supported by Science Fund of the Chinese Academy of Sciences.
Abstract：
This paper proves that the number of distinct principal curvatures of a real isoparametric hypersurface in $\[C{P^n}\]$ with constant principal curvatures can be only 2, 3 or 5. The preimage of such hypersurface under the Hopf fibration is an isoparametric hypersurface in $\[{S^{2n + 1}}\]$ with 2 or 4 disinct principal curvatures. For real isopariametric hypersurfaces in $\[C{P^n}\]$ with 5 distinct constant principal curvatures a local structure
theorem is given.
