2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131203A linear Weingarten surface in Euclidean space ${\bf R}^3$ is a surface whose mean curvature $H$ and Gaussian curvature $K$ satisfy a relation of the form $aH+bK=c$, where $a,b,c\in {\bf R}$. Such a surface is said to be hyperbolic when $a^2+4bc<0$. In this paper we classify all rotational linear Weingarten surfaces of hyperbolic type. As a consequence, we obtain a family of complete hyperbolic linear Weingarten surfaces in ${\bf R}^3$ that consists into periodic surfaces with self-intersections.15 pages, 4 figuresDifferential GeometryClassical Analysis and ODEs53A10; 49Q05; 35L70; 35Q53text