The surfaces of Galileo's 4-dimensional space-time. Total curvature of the surface

The first results on the theory of surfaces of 4-dimensional Galilean space-time have been obtained. Surfaces having Galilean tangent planes are considered. The first and second quadratic shapes of the surface and the normal curvature of the surface are introduced. The classification of ordinary surface points is carried out. The total and average curvature of the surface are calculated.