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Solves Problem B on classifying umbilic-free hypersurfaces in the unit sphere, establishing new geometric insights.
In this paper, we solved Problem B raised recently by Zhai-Mo-Hu [Internat. J. Math. 36 (2025), no. 11, Art. 2550038]. As a direct consequence we obtain a complete classification for all umbilic-free hypersurfaces of the (n + 1)-dimensional unit sphere 𝕊 n+1 (n ≥ 3) with semi-parallel Blaschke tensor.
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Zhai et al. (2026) studied this question.
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