Flat Projective Planes whose Automorphism Group Contains R 2

A flat projective plane is a topological projective plane (see e.g. [3]) whose point space is a 2-manifold. Equivalently, it may be defined as the geometric and topological completion of a flat affine plane. This is a system ℒA of curves (= closed homeomorphic images of the real line R) in the euclidean plane P A = R 2 such that (1) any two different points are contained in a unique curve, and (2) the parallel axiom holds.