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.
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Setsuo Nagai (2015) studied this question.
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