Tang, Zizhou Isoparametric hypersurfaces with four distinct principal curvatures. (English) Zbl 0746.53047 Chin. Sci. Bull. 36, No. 15, 1237-1240 (1991). The main theorem of this paper is the following: Let \(M\subset S^{n+1}\) be an isoparametric hypersurface with 4 distinct principal curvatures having multiplicities \((m_ +,m_ -)\), \(m_ -\leq m_ +\). Then either \(m_ -\in\{1,2,4,8\}\) or \(m_ -+m_ ++1\) is divisible by \(2^ k=\min\{2^ \sigma\mid 2^ \sigma > m_ -,\;\sigma\in\mathbb{N}\}\). This sharpens a result of U. Abresch [Math. Ann. 264, 283-302 (1983; Zbl 0505.53027)]. Reviewer: U.Pinkall (Berlin) Cited in 8 Documents MSC: 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 53C40 Global submanifolds Keywords:isoparametric hypersurfaces Citations:Zbl 0514.53050; Zbl 0505.53027 PDFBibTeX XMLCite \textit{Z. Tang}, Chin. Sci. Bull. 36, No. 15, 1237--1240 (1991; Zbl 0746.53047)