On the surfaces of Lorentz manifold whose normal bundles have special properties
type: Item
instance of: scholarly article
title: On the surfaces of Lorentz manifold whose normal bundles have special properties
zbMATH Open document ID: 0548.53025
DOI: 10.1007/BF01781074
author: N. E. Zubov
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1983-01-01T00:00:00Z
review text: Let S be a surface of the manifold \({\mathbb{R}}^ 3\) provided with the Lorentz metric \(ds^ 2=dx^ 2+dy^ 2-dz^ 2\). The aim of the present paper is to study such a surface S having the property that its normals establish an area preserving representation between the two sheets of the evolute \(S_ 1\), \(S_ 2\) of S. The main results can be stated as follows. The catenoid is the only minimal surface of the Lorentz manifold defined above with this property.
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 3874132
zbMATH Keywords: surface
zbMATH Keywords: area preserving representation
zbMATH Keywords: evolute
zbMATH Keywords: Lorentz manifold
MaRDI profile type: Publication
cites work: Q5790826
cites work: Sur les surfaces à courbure moyenne constante applicables sur des surfaces de revolution
cites work: Q5520492
cites work: Q4064639
cites work: Q3756913
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cites work: General Relativity for Mathematicians
full work available at URL: https://doi.org/10.1007/bf01781074
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description: scientific article; zbMATH DE number 3874132