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Surfaces of Constant Curvature in the Pseudo-Galilean Space

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  • Željka Milin Šipuš
  • Blaženka Divjak

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.

Suggested Citation

  • Željka Milin Šipuš & Blaženka Divjak, 2012. "Surfaces of Constant Curvature in the Pseudo-Galilean Space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-28, October.
    • Handle: RePEc:hin:jijmms:375264
    DOI: 10.1155/2012/375264
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