Biharmonic maps between warped product manifolds

Biharmonic maps between warped products are studied. The main results are: (i) the condition for the biharmonicity of the inclusion of a Riemannian manifold N into the warped product M ×f 2 theprojectionπ : M×f2 N → M; N and of (ii) the construction of two new classes of non-harmonic biharmonic maps using products of harmonic maps φ = 1M × ψ : M × N → M × N and warping the metric on their domain or codomain; (iii) the study of three classes of axially symmetric biharmonic maps, using the warped product setting.