Index of minimal hypersurfaces in real projective spaces
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909075237765120 |
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| author | Chen, Shuli |
| author_facet | Chen, Shuli |
| contents | We prove that for an embedded unstable one-sided minimal hypersurface of the $(n+1)$-dimensional real projective space, the Morse index is at least $n+2$, and this bound is attained by the cubic isoparametric minimal hypersurfaces. We also show that there exist closed embedded two-sided minimal surfaces in the 3-dimensional real projective space of each odd index by computing the index of the Lawson surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02932 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Index of minimal hypersurfaces in real projective spaces Chen, Shuli Differential Geometry We prove that for an embedded unstable one-sided minimal hypersurface of the $(n+1)$-dimensional real projective space, the Morse index is at least $n+2$, and this bound is attained by the cubic isoparametric minimal hypersurfaces. We also show that there exist closed embedded two-sided minimal surfaces in the 3-dimensional real projective space of each odd index by computing the index of the Lawson surfaces. |
| title | Index of minimal hypersurfaces in real projective spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2301.02932 |