Linear Weingarten surfaces in Euclidean and hyperbolic space
نویسنده
چکیده
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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