Ki and Nakagawa [Tôhoku Math. J., 39, 27-40 (1987)] characterized the minimal isoparametric hypersurfaces in a sphere that have three distinct constant principal curvatures from the stand point of the Ricci tensor. In this paper we generalize their results and characterize the isoparametric hypersurfaces, again in a sphere and with three distinct constant principal curvatures, that are either minimal or parallel to a minimal hypersurface.
"A characterization of isoparametric hypersurfaces in a sphere with $g\le 3$." Tsukuba J. Math. 38 (2) 207 - 225, March 2015. https://doi.org/10.21099/tkbjm/1429103722