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arXiv · 0809.3821

Parabolic Weingarten surfaces in hyperbolic space

Rafael López
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Abstract

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 $aκ_1+bκ_2=c$ or $aH+bK=c$, where $a,b,c\in \r$ and, as usual, $κ_i$ 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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Rafael López. 2008-09-22. Parabolic Weingarten surfaces in hyperbolic space. https://arxiv.org/abs/0809.3821

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