Galileo's space-time surfaces according to the Christoffel symbols

The definability of the metric function of the surface of the 3-dimensional Galilean space-time by the Christoffel symbols has been established, which means that the determinability of the first quadratic shape of the surface by the Christoffel symbols has also been established. Examples of obtaining a metric function using specified Christoffel symbols are given. Surfaces are isometric only if they have the same Christoffel symbols. The surfaces defined by the Christoffel symbols and the surfaces for which there are no isometric (non-bending surfaces) are indicated. An example of a class of Galilean space surfaces with a Euclidean metric function is considered. The expression of the total curvature of the surface is obtained in terms of the Christoffel symbols.