Biharmonic maps between warped product manifolds

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A short survey on biharmonic maps between Riemannian manifolds (2005, background): “Another important class of biharmonic Riemannian submersions was described in [7] and it is descried as follows.”
Some constructions of biharmonic maps and Chen's conjecture on biharmonic hypersurfaces (2009, unknown): “Biharmonic maps which are neither conformal immersions nor horizontally weakly conformal maps: (i) The composition of the Hopf map and the inclusion: S(3)( 1 √ 2 ) −→ S(2)( 1 √ 2 ) →֒ S(3) ([18]), and more generally, the pull-backs of proper biharmonic maps S( 1 √ 2 ) →֒ S(m = 2, 4, 8) by the Hopf f”
The stress-energy tensor for biharmonic maps (2006, background): “When ln f is affine, grad(ln f ) is Killing of constant norm ([5]), hence π is biharmonic.”
Biharmonic hypersurfaces in Riemannian manifolds (2009, methodology): “4 in [3] which was proved by a different method.”