Isometric immersions of tori into \(\mathbb{R}^ 3\) with given mean curvature
type: Item
instance of: scholarly article
title: Isometric immersions of tori into \(\mathbb{R}^ 3\) with given mean curvature
zbMATH Open document ID: 0761.53005
DOI: 10.1007/BF03323088
author: Shing H. Doong
author: Ioannis Markos Roussos
published in: Results in Mathematics
publication date: 1992-09-27T00:00:00Z
review text: It is known that a compact Riemannian surface can admit at most two geometrically distinct isometric immersions into \(\mathbb{R}^ 3\) with given non-constant mean curvature. If the genus is zero, then there is at most one such immersion. The authors consider the question if the at most two immersions can be reduced to at most one for surfaces of genus 1. A positive answer is given for three particular types of surfaces of genus 1.
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 62171
zbMATH Keywords: congruent immersions
zbMATH Keywords: isometric immersions
zbMATH Keywords: non-constant mean curvature
reviewed by: Barbara Opozda
MaRDI profile type: Publication
cites work: An Elementary Proof of the Existence of Isothermal Parameters on a Surface
cites work: On the mean curvature function for compact surfaces
cites work: On the Number of Distinct Isometric Immersions of a Riemannian Surface Into R 3 with Given Mean Curvature
cites work: Q3342966
cites work: A characterization of tori with constant mean curvature in space form
full work available at URL: https://doi.org/10.1007/bf03323088
OpenAlex ID: W2074116275
description: scientific article; zbMATH DE number 62171