  In this work we study the dimensional reduction of smooth circle invariant
Yang-Mills instantons defined on 4-manifolds which are non-trivial circle
fibrations over hyperbolic 3-space. A suitable choice of the 4-manifold metric
within a specific conformal class gives rise to singular and smooth hyperbolic
monopoles. A large class of monopoles is obtained if the conformal factor
satisfies the Helmholtz equation on hyperbolic 3-space. We describe simple
configurations and relate our results to the JNR construction, for which we
provide a geometric interpretation.
