Curves in Riemannian Manifolds Making Prescribed Angles With Torse-Forming Vector Fields
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917368625627136 |
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| author | Aydin, Muhittin Evren Dilmen, Esra Karakaya, Busra |
| author_facet | Aydin, Muhittin Evren Dilmen, Esra Karakaya, Busra |
| contents | In this paper, we introduce the notion of a prescribed angle curve in a Riemannian manifold associated with a pair $(\mathcal{V},θ)$, where $\mathcal{V}$ is a unit vector field along the curve and $θ$ denotes the angle between $\mathcal{V}$ and the principal normal vector of the curve. When $\mathcal{V}$ is a torse-forming vector field, we establish an existence result for prescribed angle curves. In the $3$-dimensional case, we determine the curvatures of these curves in terms of the prescribed angle and the potential function of $\mathcal{V}$. Moreover, using this notion, we provide a new characterization of curves lying on geodesic spheres in real space forms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_28072 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Curves in Riemannian Manifolds Making Prescribed Angles With Torse-Forming Vector Fields Aydin, Muhittin Evren Dilmen, Esra Karakaya, Busra Differential Geometry 53A04, 53B20 In this paper, we introduce the notion of a prescribed angle curve in a Riemannian manifold associated with a pair $(\mathcal{V},θ)$, where $\mathcal{V}$ is a unit vector field along the curve and $θ$ denotes the angle between $\mathcal{V}$ and the principal normal vector of the curve. When $\mathcal{V}$ is a torse-forming vector field, we establish an existence result for prescribed angle curves. In the $3$-dimensional case, we determine the curvatures of these curves in terms of the prescribed angle and the potential function of $\mathcal{V}$. Moreover, using this notion, we provide a new characterization of curves lying on geodesic spheres in real space forms. |
| title | Curves in Riemannian Manifolds Making Prescribed Angles With Torse-Forming Vector Fields |
| topic | Differential Geometry 53A04, 53B20 |
| url | https://arxiv.org/abs/2603.28072 |