Torqued and Anti-Torqued Vector Fields on Hyperbolic Spaces
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909646522941440 |
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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 study the existence of torqued and anti-torqued vector fields on the hyperbolic ambient space $\mathbb{H}^n$. Although there are examples of proper torqued vector fields on open subsets of $\mathbb{H}^n$, we prove that there is not a proper torqued vector field globally defined on $\mathbb{H}^n$. Similarly, we have another non-existence result for anti-torqued vector fields as long as their conformal scalar is a non-constant function satisfying certain conditions. When the conformal scalar is constant, some examples of anti-torqued vector fields are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torqued and Anti-Torqued Vector Fields on Hyperbolic Spaces Aydin, Muhittin Evren Mihai, Adela Özgür, Cihan Differential Geometry 53B20, 53C24, 53C25 In this paper, we study the existence of torqued and anti-torqued vector fields on the hyperbolic ambient space $\mathbb{H}^n$. Although there are examples of proper torqued vector fields on open subsets of $\mathbb{H}^n$, we prove that there is not a proper torqued vector field globally defined on $\mathbb{H}^n$. Similarly, we have another non-existence result for anti-torqued vector fields as long as their conformal scalar is a non-constant function satisfying certain conditions. When the conformal scalar is constant, some examples of anti-torqued vector fields are provided. |
| title | Torqued and Anti-Torqued Vector Fields on Hyperbolic Spaces |
| topic | Differential Geometry 53B20, 53C24, 53C25 |
| url | https://arxiv.org/abs/2504.13514 |