This analysis uncovers features of hopf hypersurfaces with constant principal curvatures, indicating crucial classification for curvatures.
In this paper, we study the Hopf hypersurfaces of the complex hyperbolic quadric Qm*=SOᵒ2,m/(SO₂× SOₘ) (m≥3) with constant principal curvatures. We classify the Hopf hypersurfaces of Qm* (m≥3) with at most two distinct constant principal curvatures. For Hopf hypersurfaces with three or four distinct constant principal curvatures, we determine the values of the principal curvatures as well as their multiplicities.
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Li et al. (2025) studied this question.
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