Surfaces of Constant Curvature in the Pseudo-Galilean Space

Željka Milin Šipuš and Blaženka Divjak

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-28

Abstract:

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:375264

DOI: 10.1155/2012/375264

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