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Abstract. 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 3 ⊂ ¼ 3 over the future light cone3 , x 3 > 0} in 3-dimensional space-time.

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For every real-analytic CR-manifold M we give necessary and sufficient conditions that M can be realized in a suitable neighbourhood of a given point a ∈ M as a tube submanifold of some C r . We clarify the question of the 'right' equivalence between two local tube realizations of the CR-manifold germ (M, a) by introducing two different notions of affine equivalence. One of our key results is a procedure that reduces the classification of equivalence classes to a purely algebraic manipulation in terms of Lie theory.

Abstract. -A real form G of a complex semi-simple Lie group G C has only finitely many orbits in any given G C -flag manifold Z = G C /Q. The complex geometry of these orbits is of interest, e.g., for the associated representation theory. The open orbits D generally possess only the constant holomorphic functions, and the relevant associated geometric objects are certain positive-dimensional compact complex submanifolds of D which, with very few well-understood exceptions, are parameterized by the Wolf cycle domains Ω W (D) in G C /K C , where K is a maximal compact subgroup of G. Thus, for the various domains D in the various ambient spaces Z, it is possible to compare the cycle spaces Ω W (D). The main result here is that, with the few exceptions mentioned above, for a fixed real form G all of the cycle spaces Ω W (D) are the same. They are equal to a universal domain Ω AG which is natural from the the point of view of group actions and which, in essence, can be explicitly computed. The essential technical result is that if b Ω is a G-invariant Stein domain which contains Ω AG and which is Kobayashi hyperbolic, then b Ω = Ω AG . The equality of the cycle domains follows from the fact that every Ω W (D) is itself Stein, is hyperbolic, and contains Ω AG . FELS (G.) & HUCKLEBERRY (A.)Résumé (Caractérisation de domaines de cycles par l'hyperbolicité au sens de Kobayashi) Une forme réelle G d'un groupe de Lie semi-simple G C n'admet qu'un nombre fini d'orbites dans toute G C -variété de drapeaux Z = G C /Q. La géométrie complexe de ces orbites est intéressante, par exemple pour la théorie de la représentation associée. Les fonctions holomorphes sur les orbites ouvertes D de G sont constantes en général ; les objets géométriques importants liésà ces orbites sont des sous-variétés complexes de D de dimension positives qui,à quelques rares exceptions bien comprises, sont paramétrées par les domaines de cycles de Wolf Ω W (D) ∈ G C /K C , où K est un sous-groupe maximal compact de G. Alors, pour les domaines D dans les variétés ambiantes Z, il est possible de comparer les domaines de cycles Ω W (D