Surfaces in Minkowski 3-space on which H and K are linearly related
type: Item
instance of: scholarly article
title: Surfaces in Minkowski 3-space on which H and K are linearly related
zbMATH Open document ID: 0553.53032
author: Tilla Weinstein
published in: Michigan Mathematical Journal
publication date: 1983-01-01T00:00:00Z
review text: The paper is a study of surfaces in \(M^ 3\), a Minkowski 3-space, whose mean curvature H and extrinsic curvature K satisfy a non-trivial linear relationship \(\alpha +\beta H+\gamma K\equiv 0\), where \(\alpha\), \(\beta\), \(\gamma\) are constants. As an example of the results given in the paper we state the following: A spacelike or timelike surface in \(M^ 3\) on which \(\alpha +\beta H+\gamma K\equiv 0\), with \(\beta^ 2\neq 4\alpha \gamma\), is equidistant from at least one surface with H or K constant. This is an extension of the classical theorem of Bonnet, which associates an equidistant surface of constant \(K>0\) (resp. \(H\neq 0)\) to a surface of constant \(H\neq 0\) (resp. \(K>0)\).
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53A07
zbMATH DE Number: 3881434
zbMATH Keywords: Minkowski space
zbMATH Keywords: surfaces
zbMATH Keywords: mean curvature
zbMATH Keywords: extrinsic curvature
reviewed by: Thomas Hasanis
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029002907
OpenAlex ID: W2089698703
DOI: 10.1307/MMJ/1029002907
description: scientific article; zbMATH DE number 3881434