Oduli Li transformations. Trajectories and trajectory surfaces. The proper geometry of the surface

The trajectories of geometric transformations are obtained by the odular method. The properties of transformation trajectories are investigated. The surfaces of the trajectories, in particular the odular surfaces of the trajectories, are obtained, and their geodesics are indicated. These surfaces have their own geometry - odular, it is different from the internal geometry of the surface. The odular surface of the trajectories, an analogue of the affine plane, may have nonzero Gaussian curvature.