Abstract
The subject of this article is the set of complex manifolds X whose group of automorphisms (of biholomorphic transformations) acts transitively on X. The list of one-dimensional complex manifolds having this property was surely known already to Poincaré. It consists of the complex plane C, the punctured plane C* = ℂ\{0}, the unit disc in C, the Riemann sphere, and one-dimensional complex tori (elliptic curves). In each of these cases it is easy to calculate the automorphism group and to see that it is a Lie group of transformations of the manifold X.KeywordsComplex ManifoldParabolic SubgroupStein ManifoldHermitian Symmetric SpaceHomogeneous ManifoldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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