TORQUED AND ANTI-TORQUED VECTOR FIELDS ON HYPERBOLIC SPACES

Abstract

In this paper, we study the existence of torqued and anti-torqued vector fields on the hyperbolic ambient space $\h^n$. Although there are examples of proper torqued vector fields on open subsets on $\h^n$, we prove that there is no a proper torqued vector field globally defined on $\h^n$. Similarly, we have another non-existence result for anti-torqued vector fields  as long as their conformal scalar is a non-constant function. When the conformal scalar is constant some examples of anti-torqued vector fields are provided.