Surfaces of Constant Curvature in the Pseudo-Galilean Space

Surfaces of Constant Curvature in the Pseudo-Galilean Space

We develop the local theory of surfaces immersed in the pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo-Galilean space is provided. We describe sur...

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Main Authors: Željka Milin Šipuš, Blaženka Divjak
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2012/375264
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spelling doaj-b434feac7fc24ae6bd9b4ec68d2bae152020-11-24T22:33:29ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/375264375264Surfaces of Constant Curvature in the Pseudo-Galilean SpaceŽeljka Milin Šipuš0Blaženka Divjak1Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička Cesta 30, 10 000 Zagreb, CroatiaFaculty of Organization and Informatics, University of Zagreb, Pavlinska 2, 42 000 Varaždin, CroatiaWe develop the local theory of surfaces immersed in the pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo-Galilean space is provided. We describe surfaces of revolution of constant curvature. We introduce special local coordinates for surfaces of constant curvature, so-called the 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.http://dx.doi.org/10.1155/2012/375264
collection DOAJ
language English
format Article
sources DOAJ
author Željka Milin Šipuš
Blaženka Divjak
spellingShingle Željka Milin Šipuš
Blaženka Divjak
Surfaces of Constant Curvature in the Pseudo-Galilean Space
International Journal of Mathematics and Mathematical Sciences
author_facet Željka Milin Šipuš
Blaženka Divjak
author_sort Željka Milin Šipuš
title Surfaces of Constant Curvature in the Pseudo-Galilean Space
title_short Surfaces of Constant Curvature in the Pseudo-Galilean Space
title_full Surfaces of Constant Curvature in the Pseudo-Galilean Space
title_fullStr Surfaces of Constant Curvature in the Pseudo-Galilean Space
title_full_unstemmed Surfaces of Constant Curvature in the Pseudo-Galilean Space
title_sort surfaces of constant curvature in the pseudo-galilean space
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2012-01-01
description We develop the local theory of surfaces immersed in the pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo-Galilean space is provided. We describe surfaces of revolution of constant curvature. We introduce special local coordinates for surfaces of constant curvature, so-called the 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.
url http://dx.doi.org/10.1155/2012/375264
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AT blazenkadivjak surfacesofconstantcurvatureinthepseudogalileanspace
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