ROTATIONAL LINEAR WEINGARTEN SURFACES OF HYPERBOLIC TYPE BY

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 a2 + 4bc < 0. In this paper we study rotational linear Weingarten surfaces of hyperbolic type giving a classification under suitable hypoth-esis. 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. 1