Abstract
We construct biharmonic nonharmonic maps between Riemannian manifoldsM and N by first making the ansatz that ϕM → N be aharmonic map and then deforming the metric conformally on M to renderϕ biharmonic. The deformation will, in general, destroy theharmonicity of ϕ. 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.
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Baird, P., Kamissoko, D. On Constructing Biharmonic Maps and Metrics. Annals of Global Analysis and Geometry 23, 65–75 (2003). https://doi.org/10.1023/A:1021213930520
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DOI: https://doi.org/10.1023/A:1021213930520