Surfaces of constant curvature in the pseudo-Galilean space
type: Item
instance of: scholarly article
title: Surfaces of constant curvature in the pseudo-Galilean space
zbMATH Open document ID: 1255.53017
DOI: 10.1155/2012/375264
author: Željka Milin Šipuš
author: Blaženka Divjak
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2012-12-18T00:00:00Z
review text: Summary: We develop the local theory of surfaces immersed in pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian and mean curvatures. By this, the general setting for the study of surfaces of constant curvature in pseudo-Galilean space is provided. We describe surfaces of revolution of constant curvature. We introduce special local coordinates for surfaces of constant curvature, the so-called Tchebyshev coordinates, and show that the angle between parametric curves satisfies the Klein-Gordon partial differential equation. We determine the Tchebyshev coordinates for surfaces of revolution and construct a surface with constant curvature from a particular solution of the Klein-Gordon equation.
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 6116539
zbMATH Keywords: curvature
zbMATH Keywords: surfaces of revolution
zbMATH Keywords: constant curvature
zbMATH Keywords: Tchebyshev coordinates
zbMATH Keywords: Klein-Gordon equation
Wikidata QID: Q58705801
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/375264
OpenAlex ID: W2048714264
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DBLP publication ID: journals/ijmmsc/SipusD12
description: scientific article; zbMATH DE number 6116539