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Isoparametric hypersurfaces with four principal curvatures. IV. (English) Zbl 1455.53081

In this nice and well-written paper, the author completes the classification of isoparametric hypersurfaces in spheres initiated by E. Cartan. He shows that an isoparametric hypersurface with four principal curvatures and multiplicity pair \((7,8)\) is either the one constructed by H. Ozeki and M. Takeuchi [Tohoku Math. J. (2) 27, 515–559 (1975; Zbl 0359.53011)], or one of the two constructed by D. Ferus et al. [Math. Z. 177, 479–502 (1981; Zbl 0443.53037)].
For Part I, see [T. E. Cecil et al., Ann. Math. (2) 166, No. 1, 1–76 (2007; Zbl 1143.53058)], for Part II, see [the author, Nagoya Math. J. 204, 1–18 (2011; Zbl 1243.53094)] and for Part III, see [the author, Nagoya Math. J. 204, 1–18 (2011; Zbl 1243.53094)].

MSC:

53C40 Global submanifolds
53A07 Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces
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References:

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