2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221296In the half-space model of hyperbolic space, that is, $\r^3_{+}=\{(x,y,z)\in\r^3;z>0\}$ with the hyperbolic metric, a translation surface is a surface that writes as $z=f(x)+g(y)$ or $y=f(x)+g(z)$, where $f$ and $g$ are smooth functions. We prove that the only minimal translation surfaces (zero mean curvature in all points) are totally geodesic planes.8 pagesDifferential Geometry53A10text