This is the diploma thesis of Jörg Winkelmann. The subject is to classify all complex manifolds X of dimension three on which a complex Lie group G acts transitively by a holomorphic action G x X -> X. All quotients of SL2C by discrete subgroups are labeled as one class, but besides this exception a fine classification (as complex manifolds) is obtained. The Diplomarbeit is written in german.
A survey (in french) appeared in
Classification des espaces complexes homogenès de dimension 3. I & II. C.R. Acad. Sci. Paris 306, 231-234 & 405-408 (1988).
The whole material is covered in
The Classification of three-dimensional homogeneous complex manifolds. Springer Verlag Hamburg Berlin Heidelberg. LN 1602
(this book is written in english).