i'm getting somewhat confused about the relationship between "(generalized...) de sitter space" and "the conformal compactification of pseudo-euclidean (t,s)-space" ...
i have a pretty strong feeling that there _is_ a relationshship... hmmm... ??something about non-degenerate hyperboloid vs projective degenerate hyperboloid, or something?? ??something about the general idea of obtaining some sort of space-time (or something... metrically or conformally structured, perhaps...) as some sort of "hyperboloid" in a larger space-time ... ???or something like that??

??for some reason this is reminding me of that business about... ??how did it go??... co-/adjoint orbits stable under scalar multiplication, treated projectively, getting contact structure, vs unstable ones, treated projectively, keeping something like symplectic structure... ??????? or something???.....