The classification of homogeneous surfaces (Q1084235)

A homogeneous surface is a two-dimensional complex manifold on which a Lie group acts transitively as a group of biholomorphic transformations. The author gives a full and selfcontained proof of the classification of homogeneous surfaces. The steps leading to this classification were done by a number of people and are scattered around in the literature. Many of the proofs are more elegant than in the original papers. The article gives a general introduction to the methods and problems of the theory of homogeneous complex manifolds. Recently, Jörg Winkelmann managed to give a complete classification of all three-dimensional homogeneous complex manifolds [\textit{J. Winkelmann}, Thesis, Bochum 1987].