KLEINIAN CHARACTERIZATION OF ASYMPTOTIC SYMMETRIES OF REAL GENERAL-RELATIVITY

According to Klein's Erlanger programme, one may (indirectly) specify a geometry by giving a group action. Conversely, given a group action, one may ask for the corresponding geometry. Recently, I showed that t he real asymptotic symmetry groups of general relativity (in any signa ture) have natural 'projective' classical actions on suitable 'Radon t ransform' spaces of affine 3-planes in flat 4-space. In this paper, I give concrete models for these groups and actions. Also, for the 'atom ic' cases, I give geometric structures for the spaces of affine 3-plan es for which the given actions are the automorphism groups.