Surfaces of Constant Curvature in the Pseudo-Galilean Space

Abstract EN

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.