In this paper, we classify the hypersurfaces in and , , with distinct constant principal curvatures, , where and denote the sphere and hyperbolic space of dimension , respectively. We prove that such hypersurfaces are isoparametric in those spaces. Furthermore, we find a necessary and sufficient condition for an isoparametric hypersurface in and with flat normal bundle when regarded as submanifolds with codimension two of the underlying flat spaces and , having constant principal curvatures.
"Hypersurfaces with constant principal curvatures in and ." Illinois J. Math. 63 (4) 551 - 574, December 2019. https://doi.org/10.1215/00192082-8018599