Prescribed Angle Surfaces Associated with Torse-Forming Vector Fields in Riemannian Manifolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914551268638720 |
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| author | Aydın, Muhittin Evren Dilmen, Esra Karakaya, Büşra |
| author_facet | Aydın, Muhittin Evren Dilmen, Esra Karakaya, Büşra |
| contents | In this paper, we introduce the notion of a prescribed angle hypersurface in a Riemannian manifold associated with a pair $(\mathcal{V},θ)$, where $\mathcal{V}$ is a unit vector field along the hypersurface and $θ$ denotes the angle between $\mathcal{V}$ and the unit normal vector field of the hypersurface. We study such hypersurfaces in case $\mathcal{V}$ is a torse-forming vector field. In the particular $3$-dimensional case, we determine the intrinsic and extrinsic curvatures of these hypersurfaces in terms of the prescribed angle and the potential function of $\mathcal{V}$. Using this, we classify prescribed angle surfaces under suitable assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Prescribed Angle Surfaces Associated with Torse-Forming Vector Fields in Riemannian Manifolds Aydın, Muhittin Evren Dilmen, Esra Karakaya, Büşra Differential Geometry 53B20, 53A05, 53C42 In this paper, we introduce the notion of a prescribed angle hypersurface in a Riemannian manifold associated with a pair $(\mathcal{V},θ)$, where $\mathcal{V}$ is a unit vector field along the hypersurface and $θ$ denotes the angle between $\mathcal{V}$ and the unit normal vector field of the hypersurface. We study such hypersurfaces in case $\mathcal{V}$ is a torse-forming vector field. In the particular $3$-dimensional case, we determine the intrinsic and extrinsic curvatures of these hypersurfaces in terms of the prescribed angle and the potential function of $\mathcal{V}$. Using this, we classify prescribed angle surfaces under suitable assumptions. |
| title | Prescribed Angle Surfaces Associated with Torse-Forming Vector Fields in Riemannian Manifolds |
| topic | Differential Geometry 53B20, 53A05, 53C42 |
| url | https://arxiv.org/abs/2605.09553 |