CR-manifolds of dimension 5: A Lie algebra approach

We study real-analytic Levi degenerate hypersurfaces M in complex manifolds of dimension 3, for which the CR-automorphism group Aut(M) is a real Lie group acting transitively on M . We provide large classes of examples for such M , compute the corresponding groups Aut(M) and determine the maximal subsets of M that cannot be separated by global continuous CR-functions. It turns out that all our examples, although partly arising in different contexts, are locally CR-equivalent to the tube T = C × i’ ⊂ ƒ over the future light cone C := {x ∈ ’ : x1 + x2 = x3, x3 > 0} in 3-dimensional space-time.