The generalized warped product and the biharmonic maps

Purpose In the first, we consider a smooth map and we calculate the bitension field of the map as a consequence, we treat the biharmonicity of the second projection. In a second result, the objective of the study is to the biharmonicity of the identity map and we give some particular cases. In the last part, we study the biharmonicity of the inclusion map. With this setting we obtain new examples of biharmonic non-harmonic maps. Design/methodology/approach We give the relation between the curvature tensor fields of the generalized warped product by using the Levi-Civita connection. We give the harmonic and the biharmonic equation for some particular cases. We obtain new examples of biharmonic non-harmonic maps. Findings We study the biharmonicity of several cases and we construct some new examples of biharmonic non-harmonic maps. Originality/value Characterization of the biharmonicity using the Generalized warped product. Construction of New Examples of biharmonic non-harmonic maps.