Rotational linear Weingarten surfaces of hyperbolic type

A linear Weingarten surface in Euclidean space ℝ³ is a surface whose mean curvature H and Gaussian curvature K satisfy a relation of the form aH + bK = c, where a, b, c ∈ ℝ. Such a surface is said to be hyperbolic when a ² + 4bc < 0. In this paper we study rotational linear Weingarten surfaces of hyperbolic type giving a classification under suitable hypothesis. As a consequence, we obtain a family of complete hyperbolic linear Weingarten surfaces in ℝ³ that consists of surfaces with self-intersections whose generating curves are periodic. Partially supported by MEC-FEDER grant no. MTM2007-61775.