Surfaces of constant curvature in the pseudo-Galilean space (Q1925552)

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