Linear Weingarten surfaces in Euclidean and hyperbolic space

Details Linear Weingarten surfaces in Euclidean and hyperbolic space Linear Weingarten surfaces in Euclidean and hyperbolic space

2009-06-17

arxiv.org/abs/0906.3302v1

Mathematics

Differential Geometry

13 pages, 3 figures. to appear in Matematica Contemporanea

Scientific paper

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.

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