Biharmonic maps between doubly warped product manifolds

In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds Band F into the nontrivial (proper) doubly warped product manifold (f)B x(b) F cannot be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections (f)B x(b) F -> B and (f)B x(b) F -> F, respectively. Some characterizations for non-harmonic biharmonic maps are given by using product of harmonic maps and warping metric. Especially, in the case of f = 1, the results for warped product in [4] are obtained.