Analogues of Rossi's map and E. Cartan's classification of homogeneous strongly pseudoconvex 3-dimensional hypersurfaces
We introduce analogues of a map due to Rossi and show how they can be used to explicitly determine all covers of certain homogeneous strongly pseudoconvex 3-dimensional hypersurfaces that appear in the classification obtained by E. Cartan in 1932.
2 9 A ug 2 00 5 Hyperbolic 2-Dimensional Manifolds with 3-Dimensional Automorphism Groups I
Let M be a Kobayashi-hyperbolic 2-dimensional complex manifold and Aut(M) the group of holomorphic automorphisms of M . We showed earlier that if dimAut(M) = 3, then Aut(M)-orbits are closed submanifolds in M of (real) codimension 1 or 2. In this paper we classify all connected Kobayashi-hyperbolic 2-dimensional manifolds with 3-dimensional automorphism groups in the case when every orbit has codimension 1. A classification in the case when codimension 2 orbits are present will appear elsewhere.
Examples of unbounded homogeneous domains in complex space
We present several examples of homogeneous domains in complex space that do not have bounded realisations. The domains are equivalent to tubes over affinely homogeneous domains in real space.