Minimal Hypersurfaces with constant scalar curvature in $\mathbf{S}^6$
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866916034931326976 |
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| author | Tao, Ya |
| author_facet | Tao, Ya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19495 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimal Hypersurfaces with constant scalar curvature in $\mathbf{S}^6$ Tao, Ya Differential Geometry 53C12, 53C20, 53C40 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. |
| title | Minimal Hypersurfaces with constant scalar curvature in $\mathbf{S}^6$ |
| topic | Differential Geometry 53C12, 53C20, 53C40 |
| url | https://arxiv.org/abs/2605.19495 |