On constructing biharmonic maps and metrics

We construct biharmonic nonharmonic maps between Riemannian manifolds M and N by first making the ansatz that omega: M --> N be a harmonic map and then deforming the metric conformally on M to render omega biharmonic. The deformation will, in general, destroy the harmonicity of omega. We call a metric which renders the identity map biharmonic, a biharmonic metric. On an Einstein manifold, the only conformally equivalent biharmonic metrics are defined by isoparametric functions.