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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2507.22526 |
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| _version_ | 1866915417650364416 |
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| author | Anarella, Mateo D'haene, Marie |
| author_facet | Anarella, Mateo D'haene, Marie |
| contents | In the context of six-dimensional homogeneous nearly Kähler manifolds, we prove that $\mathbb S^6$ is the only ambient space admitting constant sectional curvature hypersurfaces. In order to do so, we prove first that in $\mathbb S^3\times\mathbb S^3$, $\mathbb C P^3$ and $F(\mathbb C^3)$, any hypersurface with constant sectional curvature is $η$-quasi umbilical, where $η$ is the dual one-form of the Reeb vector field. Then, we use the non-existence of such hypersurfaces in these spaces. Additionally, we characterize hypersurfaces of six-dimensional nearly Kähler manifolds which are Sasakian, nearly Sasakian, co-Kähler and nearly cosymplectic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hypersurfaces of six-dimensional nearly Kähler manifolds Anarella, Mateo D'haene, Marie Differential Geometry 53C42 In the context of six-dimensional homogeneous nearly Kähler manifolds, we prove that $\mathbb S^6$ is the only ambient space admitting constant sectional curvature hypersurfaces. In order to do so, we prove first that in $\mathbb S^3\times\mathbb S^3$, $\mathbb C P^3$ and $F(\mathbb C^3)$, any hypersurface with constant sectional curvature is $η$-quasi umbilical, where $η$ is the dual one-form of the Reeb vector field. Then, we use the non-existence of such hypersurfaces in these spaces. Additionally, we characterize hypersurfaces of six-dimensional nearly Kähler manifolds which are Sasakian, nearly Sasakian, co-Kähler and nearly cosymplectic. |
| title | Hypersurfaces of six-dimensional nearly Kähler manifolds |
| topic | Differential Geometry 53C42 |
| url | https://arxiv.org/abs/2507.22526 |