Deformations of Metrics and Biharmonic Maps
AbstractWe construct biharmonic non-harmonic maps between Riemannian manifolds (M, g) and (N, h) by first making the ansatz that φ : (M, g) → (N, h) be a harmonic map and then deforming the metric on N by{\tilde h_\alpha } = \alpha h + \left( {1 - \alpha } \right){\rm{d}}f \otimes {\rm{d}}fto render φ biharmonic, where f is a smooth function with gradient of constant norm on (N, h) and α ∈ (0, 1). We construct new examples of biharmonic non-harmonic maps, and we characterize the biharmonicity of some curves on Riemannian manifolds.
2008 ◽
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