International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 375264, 28 pages
Research Article

Surfaces of Constant Curvature in the Pseudo-Galilean Space

1Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička Cesta 30, 10 000 Zagreb, Croatia
2Faculty of Organization and Informatics, University of Zagreb, Pavlinska 2, 42 000 Varaždin, Croatia

Received 16 May 2012; Accepted 1 July 2012

Academic Editor: Ram U. Verma

Copyright © 2012 Željka Milin Šipuš and Blaženka Divjak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.