Parabolic Weingarten surfaces in hyperbolic space

2008/09/22 by Rafael López, López, Rafael
Mathematics · #53A10 #53C42 #53C45 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.DG #msc:53A10 #msc:53C42 #msc:53C45

paper · pdf · doi:10.48550/arxiv.0809.3821

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

arxiv created 2008/09/22 · openalex publication_date 2008/09/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

A surface in hyperbolic space \h³ invariant by a group of parabolic isometries is called a parabolic surface. In this paper we investigate parabolic surfaces of \h³ that satisfy a linear Weingarten relation of the form aκ₁+bκ₂=c or aH+bK=c, where a,b,c∈ \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.

Citations

• Parabolic surfaces in hyperbolic space with constant curvature

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