Anti-torqued slant helices and Torqued Curves in Riemannian manifolds
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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_ | 1866913799327449088 |
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| author | Aydin, Muhittin Evren Mihai, Adela Özgür, Cihan |
| author_facet | Aydin, Muhittin Evren Mihai, Adela Özgür, Cihan |
| contents | In this paper, we introduce the notion of an anti-torqued slant helix in a Riemannian manifold, defined as a curve whose principal vector field makes a constant angle with an anti-torqued vector field globally defined on the ambient manifold. We characterize and classify such curves through systems of differential equations involving their invariants. Several illustrative examples are also provided. Finally, we study torqued curves, defined as curves for which the inner product function of the principal vector field and a torqued vector field along the curve is a given constant. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_13516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anti-torqued slant helices and Torqued Curves in Riemannian manifolds Aydin, Muhittin Evren Mihai, Adela Özgür, Cihan Differential Geometry 53B20, 53A35 In this paper, we introduce the notion of an anti-torqued slant helix in a Riemannian manifold, defined as a curve whose principal vector field makes a constant angle with an anti-torqued vector field globally defined on the ambient manifold. We characterize and classify such curves through systems of differential equations involving their invariants. Several illustrative examples are also provided. Finally, we study torqued curves, defined as curves for which the inner product function of the principal vector field and a torqued vector field along the curve is a given constant. |
| title | Anti-torqued slant helices and Torqued Curves in Riemannian manifolds |
| topic | Differential Geometry 53B20, 53A35 |
| url | https://arxiv.org/abs/2504.13516 |