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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/375264 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |