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arXiv · 2504.13514

Torqued and Anti-Torqued Vector Fields on Hyperbolic Spaces

Muhittin Evren Aydin·Adela Mihai·Cihan Özgür
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Abstract

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.

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Muhittin Evren Aydin, Adela Mihai, Cihan Özgür. 2025-04-18. Torqued and Anti-Torqued Vector Fields on Hyperbolic Spaces. https://arxiv.org/abs/2504.13514

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