Some special surfaces in the pseudo-Galilean space
type: Item
instance of: scholarly article
title: Some special surfaces in the pseudo-Galilean space
zbMATH Open document ID: 1164.53007
author: Blaženka Divjak
author: Željka Milin Šipuš
published in: Acta Mathematica Hungarica
publication date: 2008-10-22T00:00:00Z
review text: A Pseudo-Galilean space \(G^1_3\) is a three-dimensional space with an absolute figure \(\{\omega,f,I\}\), where \(f\) is a line in the plane of infinity \(\omega\) and \(I\) a hyperbolic involution on \(f\). \(G^1_3\) is metrized by the projective automorphisme group of \(\{\omega,f,I\}\). In the excellently written paper the authors describe some special surfaces in \(G^1_3\) such as helical surfaces, ruled screw surfaces, surfaces of revolution and in particular tori of revolution. As a very nice result they show: Surfaces of revolution \(S_i\) in \(G^1_3\) are flat \((K\equiv 0)\) if and only if they are minimal \((H\equiv 0)\). The paper is completed by 10 interesting figures.
reviewed by: Hans Sachs
Mathematics Subject Classification ID: 53A40
Mathematics Subject Classification ID: 53A35
zbMATH DE Number: 5355880
zbMATH Keywords: pseudo-Galilean space
zbMATH Keywords: ruled surface
zbMATH Keywords: generalized screw surface
zbMATH Keywords: Gaussian curvature
zbMATH Keywords: mean curvature
MaRDI profile type: Publication
full work available at URL: s10474-007-6171-x
OpenAlex ID: W2024773681
cites work: Special curves on ruled surfaces in Galilean and pseudo-Galilean spaces
cites work: Minding isometries of ruled surfaces in pseudo-Galilean space
cites work: The projective interpretation of the eight 3-dimensional homogeneous geometries
cites work: Q5794132
cites work: Q3993400
cites work: The history of mathematics in the nineteenth century
cites work: Ruled Weingarten surfaces in Minkowski 3-space
cites work: Bergman-Vekua theory in differential form
cites work: Q3702074
cites work: Classification of ruled surfaces in Minkowski 3-spaces
DOI: 10.1007/S10474-007-6171-X
description: scientific article; zbMATH DE number 5355880