Rotational linear Weingarten surfaces of hyperbolic type

Details Rotational linear Weingarten surfaces of hyperbolic type Rotational linear Weingarten surfaces of hyperbolic type

2006-10-18

arxiv.org/abs/math/0610543v1

to appear Israel Journal of Mathematics, 2007

Mathematics

Differential Geometry

15 pages, 4 figures

Scientific paper

A linear Weingarten surface in Euclidean space ${\bf R}^3$ is a surface whose mean curvature $H$ and Gaussian curvature $K$ satisfy a relation of the form $aH+bK=c$, where $a,b,c\in {\bf R}$. Such a surface is said to be hyperbolic when $a^2+4bc<0$. In this paper we classify all rotational linear Weingarten surfaces of hyperbolic type. As a consequence, we obtain a family of complete hyperbolic linear Weingarten surfaces in ${\bf R}^3$ that consists into periodic surfaces with self-intersections.

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