Constant mean curvature planes with inner rotational symmetry in Euclidean 3-space
type: Item
instance of: scholarly article
title: Constant mean curvature planes with inner rotational symmetry in Euclidean 3-space
zbMATH Open document ID: 0799.53011
DOI: 10.1007/BF02571730
author: Martin Timmreck
author: Ulrich Pinkall
author: Dirk Ferus
published in: Mathematische Zeitschrift
publication date: 1994-05-10T00:00:00Z
full work available at URL: https://eudml.org/doc/174628
review text: Let \(({\mathbb{R}}^ 2,ds^ 2)\) be a two-dimensional Riemannian manifold admitting an isometric \(S^ 1\)-action with a fixed point \(p\). The authors prove that for each \(m\in{\mathbb{N}}\) there exists exactly a 1- parameter family of conformal isometric immersions \(f_ t: {\mathbb{R}}^ 2\to{\mathbb{R}}^ 3\) into Euclidean 3-space where \(f_ t\) has constant mean curvature and \(p\) is an umbilic of order \(m\). The authors investigate the global behaviour of \(f_ t\).
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53C10
zbMATH DE Number: 567462
zbMATH Keywords: equivariant surfaces
zbMATH Keywords: isometric \(S^ 1\)-action
zbMATH Keywords: constant mean curvature
reviewed by: V. T. Fomenko
MaRDI profile type: Publication
cites work: Singular nonlinear Cauchy problems
cites work: On the classification of constant mean curvature tori
cites work: Constant mean curvature surfaces and integrable equations
description: scientific article; zbMATH DE number 567462