Abstract
Using the method of moving frames, we prove that any irreducible Dupin hypersurface in S 5 with four distinct principal curvatures and constant Lie curvature is equivalent by Lie sphere transformation to an isoparametric hypersurface in S 5.
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Cecil, T.E., Jensen, G.R. Dupin Hypersurfaces with Four Principal Curvatures. Geometriae Dedicata 79, 1–49 (2000). https://doi.org/10.1023/A:1005008224753
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DOI: https://doi.org/10.1023/A:1005008224753