### A characterization of harmonic sections and a Liouville theorem

Let $P(M,G)$ be a principal fiber bundle and $E(M,N,G,P)$ an associated fiber bundle. Our interest is to study the harmonic sections of the projection ${\pi}_{E}$ of $E$ into $M$. Our first purpose is give a characterization of harmonic sections of $M$ into $E$ regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of ${\pi}_{E}$.