Abstract
Let X be a connected compact complex manifold. It is known, that the group Aut X of biholomorphic automorphisms of X is a complex Lie group. We call X an almost homogeneous manifold, if there is an element xo∈X and a neighbourhood U(xo) in X with the property U⊂{g(xo); g∈Aut X}. We state the following theorem: An almost homogeneous Kaehlerian manifold with vanishing first Betti number is projectiv and simply connected.
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Oeljeklaus, E. Fasthomogene Kählermannigfaltigkeiten Mit Verschwindender Erster Bettizahl. Manuscripta Math 7, 175–183 (1972). https://doi.org/10.1007/BF01679711
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DOI: https://doi.org/10.1007/BF01679711