Uncovers the non-existence of globally defined torqued vector fields in hyperbolic spaces, suggesting limits on their properties.
In this paper, we study the existence of torqued and anti-torqued vector fields on the hyperbolic ambient space Hn. Although there are examples of proper torqued vector fields on open subsets of Hn, we prove that there is not a proper torqued vector field globally defined on Hn. 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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Aydın et al. (2025) studied this question.
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