Isometric embeddings of spherical spaceforms with cyclic fundamental groups (Q1824224)

The authors give examples of compact proper-Dubin hypersurfaces that are not Lie equivalent to isoparametric hypersurfaces. The examples are constructed by deforming isoparametric hypersurfaces of FKM-type with \(g=4\) distinct principal curvatures [\textit{D. Ferus}, \textit{H. Karcher} and \textit{H.-F. Münzner}, Math. Z. 177, 479-502 (1981; Zbl 0443.53037)]. The inequivalence is proved using the Lie curvature introduced by \textit{R. Miyaoka} [Kodai Math. J. 12, No.2, 228-256 (1989)]. A similar result, proved by different methods for \(g=6\) in \(S^ 7\) is contained in [\textit{R. Miyaoka} and \textit{T. Ozawa}, Construction of taut embeddings and Cecil-Ryan conjecture (preprint, 1988)].