Biharmonic maps between warped product manifolds

Abstract

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 ×f2 N and of the projection over(π, -) : M ×f2 N → M;(ii)the construction of two new classes of non-harmonic biharmonic maps using products of harmonic maps φ{symbol} = 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. © 2006 Elsevier Ltd. All rights reserved.