On Constructing Biharmonic Maps and Metrics

We construct biharmonic nonharmonic maps between Riemannian manifoldsM and N by first making the ansatz that M N be aharmonic map and then deforming the metric conformally on M to render biharmonic. The deformation will, in general, destroy theharmonicity of . We call a metric which renders the identity mapbiharmonic, a biharmonic metric. On an Einstein manifold, theonly conformally equivalent biharmonic metrics are defined byisoparametric functions.