Parallel transport in space

Parallel translation in space is a transformation in which an arbitrary point (x; y; z) of the shape goes to a point (x + a; y + b; z + c), where the numbers a, b, are the same for all points (x; y; z).
Parallel transport in space has the following properties:
1. Parallel transfer is movement.
2. With parallel transfer, points are shifted along parallel straight lines by the same distance.
3. With parallel transfer, each straight line goes into a parallel straight line or into itself.
4. Whatever points A and A`, there is a single parallel transfer, at which point A passes to point A`.
5. In case of parallel transport in space, each plane transforms either into itself or into a plane parallel to it.