Invariant surfaces in \(\widetilde{\mathrm{PSL}}_{2}(\mathbb R, \tau)\) and applications
type: Item
instance of: scholarly article
title: Invariant surfaces in \(\widetilde{\mathrm{PSL}}_{2}(\mathbb R, \tau)\) and applications
zbMATH Open document ID: 1261.53060
author: Carlos Peñafiel
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2013-01-03T00:00:00Z
review text: The author uses a 4-dimensional isometry group of a Riemannian homogeneous 3-manifold as a Riemannian fibration over a 2-manifold with curvature equal to -1 and bundle curvature of the fibration different than 0 to study the geometric behavior of surfaces having constant mean curvature and invariant under certain one-parameter group of isometries. A number of examples is given. More precisely, the author studies rotational surfaces with constant mean curvature, minimal surfaces invariant under rotations, surfaces invariant under parabolic isometries, and surfaces invariant under hyperbolic isometries. Some theorems about existence of such surfaces are presented. Moreover, applications for rotational complete surfaces having constant mean curvature equal to \(1/2\) are developed.
reviewed by: Szymon Walczak
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 6121425
zbMATH Keywords: constant mean curvature
zbMATH Keywords: surfaces invariant by isometries
zbMATH Keywords: one-parameter group of isometries
zbMATH Keywords: minimal surfaces
MaRDI profile type: Publication
full work available at URL: s00574-012-0026-y
OpenAlex ID: W1984057240
cites work: Q5472621
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DOI: 10.1007/S00574-012-0026-Y
description: scientific article; zbMATH DE number 6121425