The Groups of Motions of Some Three-Dimensional Maximal Mobility Geometries

详细

We find the groups of motions of eight three-dimensional maximal mobility geometries. These groups are actions of just three Lie groups SL₂(R)ΔN, SL₂(C)_R, and SL₂(R)⊗SL₂(R) on the space R³, where N is a normal abelian subgroup. We also find explicit expressions for these actions.