Hypersurfaces in Riemannian manifolds with torse-forming axes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918192360718336 |
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| author | Aydın, Muhittin Evren Mihai, Adela Özgür, Cihan |
| author_facet | Aydın, Muhittin Evren Mihai, Adela Özgür, Cihan |
| contents | In this paper, we study orientable hypersurfaces $N$ in Riemannian manifolds $(M,\langle , \rangle)$ for which the inner product $\langle U, \mathcal{V} \rangle$ is constant, where $U$ is the unit normal vector field to $N$ and $\mathcal{V}$ is a globally defined torse-forming vector field on $M$, called the axis of $N$. When $\mathcal{V}$ is a unit torse-forming vector field, $N$ becomes a constant angle hypersurface with axis $\mathcal{V}$, and we classify such hypersufaces. After that, the case when $\mathcal{V}$ is a torqued vector field is considered and a corresponding classification is given. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_06370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hypersurfaces in Riemannian manifolds with torse-forming axes Aydın, Muhittin Evren Mihai, Adela Özgür, Cihan Differential Geometry 53B20, 53A07, 53C42 In this paper, we study orientable hypersurfaces $N$ in Riemannian manifolds $(M,\langle , \rangle)$ for which the inner product $\langle U, \mathcal{V} \rangle$ is constant, where $U$ is the unit normal vector field to $N$ and $\mathcal{V}$ is a globally defined torse-forming vector field on $M$, called the axis of $N$. When $\mathcal{V}$ is a unit torse-forming vector field, $N$ becomes a constant angle hypersurface with axis $\mathcal{V}$, and we classify such hypersufaces. After that, the case when $\mathcal{V}$ is a torqued vector field is considered and a corresponding classification is given. |
| title | Hypersurfaces in Riemannian manifolds with torse-forming axes |
| topic | Differential Geometry 53B20, 53A07, 53C42 |
| url | https://arxiv.org/abs/2511.06370 |