On the conformal triharmonic maps. Commun. Korean Math. Soc. Published online January 4, 2022 Seddik OUAKKAS and Yasmina REGUIG University of Saida; University of Saida Abstract : In this paper, we prove that a conformal mapping is triharmonic if and only if the gradient of its dilation is solution of a fourth-order elliptic partial differential equation and we construct some examples of triharmonic non-biharmonic maps. In this case, we also calculate the trace of the stress-energy tensor associated with the triharmonic maps. Keywords : Conformal map, Harmonic map, Biharmonic map, Triharmonic map. MSC numbers : 31B30, 58E20, 53C43, 35J48, 35J91. Full-Text :