Abstract
This paper is dedicated to Manfredo do Carmo in admiration for his mathematical achievements and his influence on the field of differential geometry of surfaces Abstract In this paper we review some author's results about Weingarten surfaces in Euclidean space R 3 and hyperbolic space H 3 . We stress here in the search of examples of linear Weingarten surfaces that satisfy a certain geometric property. First, we consider Weingarten surfaces in R 3 that are foliated by circles, proving that the surface is rotational, a Riemann example or a generalized cone. Next we classify rotational surfaces in R 3 of hyperbolic type showing that there exist surfaces that are complete. Finally, we study linear Weingarten surfaces in H 3 that are invariant by a group of parabolic isometries, obtaining its classification. MSC: 53C40, 53C50
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