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PARABOLIC AND HYPERBOLIC SCREW MOTION SURFACES IN ℍ2×ℝ

Part of: Global differential geometry

Published online by Cambridge University Press:  01 August 2008

RICARDO SA EARP
RICARDO SA EARP*
Affiliation:
Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, 22453-900 RJ, Brazil (email: earp@mat.puc-rio.br)
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Abstract

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In this paper we find many families in the product space ℍ2×ℝ of complete embedded, simply connected, minimal and surfaces with constant mean curvature H such that |H|≤1/2. We study complete surfaces invariant either by parabolic or by hyperbolic screw motions. We study the notion of isometric associate immersions. We exhibit an explicit formula for a Scherk-type minimal surface. We give a one-parameter family of entire vertical graphs of mean curvature 1/2. We prove a generalized Bour lemma that can be applied to ℍ2×ℝ,𝕊2×ℝ and to Heisenberg’s space to produce a family of screw motion surfaces isometric to a given one.

Keywords

minimal and constant mean curvature surfacesisometricassociateembeddedvertical and horizontal graphs

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 1 , August 2008 , pp. 113 - 143
Copyright
Copyright © 2008 Australian Mathematical Society

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