Parabolic Weingarten surfaces in hyperbolic space

Details Parabolic Weingarten surfaces in hyperbolic space Parabolic Weingarten surfaces in hyperbolic space

2008-09-22

arxiv.org/abs/0809.3821v1

Mathematics

Differential Geometry

22 pages, 10 figures; This work was announced in arXiv:0704.2755

Scientific paper

A surface in hyperbolic space $\h^3$ invariant by a group of parabolic isometries is called a parabolic surface. In this paper we investigate parabolic surfaces of $\h^3$ that satisfy a linear Weingarten relation of the form $a\kappa_1+b\kappa_2=c$ or $aH+bK=c$, where $a,b,c\in \r$ and, as usual, $\kappa_i$ are the principal curvatures, $H$ is the mean curvature and $K$ is de Gaussian curvature. We classify all parabolic linear Weingarten surfaces in hyperbolic space.

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