  An important theorem about biharmonic submanifolds proved independently by
Chen-Ishikawa [CI] and Jiang [Ji] states that an isometric immersion of a
surface into 3-dimensional Euclidean space is biharmonic if and only if it is
harmonic (i.e, minimal). In a later paper [CMO2], Cadeo-Monttaldo-Oniciuc shown
that the theorem remains true if the target Euclidean space is replaced by a
3-dimensional hyperbolic space form. In this paper, we prove the dual results
for Riemannian submersions, i.e., a Riemannian submersion from a 3-dimensional
space form of non-positive curvature into a surface is biharmonic if and only
if it is harmonic.
