Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1899016 | Journal of Geometry and Physics | 2006 | 17 Pages |
We study the transformation of a p-harmonic morphism into a q-harmonic morphism via biconformal change of the domain metric and/or conformal change of the codomain metric. As an application of p-harmonic morphisms, we characterize a twisted product among doubly twisted products and a warped product among twisted products using p-harmonicity of their projection maps. We describe those p-harmonic morphisms which are also biharmonic morphisms and give a complete classification of polynomial biharmonic morphisms between Euclidean spaces. Finally, we show that a horizontally homothetic harmonic morphism with harmonic energy density pulls back a nonharmonic biharmonic map to a nonharmonic biharmonic map and that totally geodesic immersing the target manifold of a nonharmonic biharmonic map into an ambient manifold produces a new nonharmonic biharmonic map. These methods are used to construct many examples of nontrivial biharmonic maps.