Dupin hypersurfaces with six principal curvatures (Q923394)

The author shows that a Dupin hypersurface with six principal curvatures is Lie equivalent to an isoparametric hypersurface if all cross ratios of sets of four principal curvatures are constant and a certain condition on the intersection properties of curvature leaves is satisfied. This continues the the author's work [ibid., No.2, 228-256 (1989; Zbl 0687.53053)] where a similar theorem was proved for Dupin hypersurfaces with four principal curvatures.