Conformal Deformation, Biharmonic and Triharmonic Maps

In this paper we present some constructions of the biharmonic maps by conformal deformation and we give some examples of proper biharmonic maps. We study a triharmonic functions where we give the equations which characterize this class of functions and we construct several examples of triharmonic non-biharmonic functions in some particular cases. In the last part of this paper, we are interested in the triharmonicity of the identity map and the results obtained allowed us to construct many examples of triharmonic non-biharmonic maps.