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arXiv · 2605.19495

Minimal Hypersurfaces with constant scalar curvature in $\mathbf{S}^6$

Ya Tao
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Abstract

In this paper, we propose certain assumptions on the principal curvatures for a closed minimal hypersurface $M^5$ in $\mathbf{S}^6$ to be isoparametric, provided that the functions $S, f_3,f_4$ are constants. Our result removes the nonnegative scalar curvature assumption as in Tang and Yan \cite{TY}. Finally, as a rigidity result, if $M^5\subset \mathbf{S}^6$ has a point with exactly two distinct principal curvatures, then it must be a Clifford torus.

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Ya Tao. 2026-05-19. Minimal Hypersurfaces with constant scalar curvature in $\mathbf{S}^6$. https://arxiv.org/abs/2605.19495

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