Homogeneous Spaces from a Complex Analytic Viewpoint

  • A. T. Huckleberry
  • E. Oeljeklaus
Part of the Progress in Mathematics book series (PM, volume 14)


Manifolds having many automorphisms play a fundamental role in geometry. If X is a compact complex manifold, then the group Aut(X) of holomorphic automorphisms of X is, when equipped with the compact-open topology, a complex Lie group. If G = Aut(X), then an orbit G(p) , p∈X, may be holomorphical ly identified with the quotient manifold G/H, where H := {g ∈ G|g(p) = p} is the isotropy group of the G-action at p. Thus, studying quotients G/H of a complex Lie group G by a closed subgroup H becomes relevant. A natural first step is to analyze the structure of compact homogeneous spaces X = G/H. In the early 1950’s, with development of Lie theory along with the theory of algebraic groups, a number of very sharp results were obtained by algebraic methods. The works of Borel (e.g., [10]), Goto [22], Tits [64] and Wang [67] are typical of this direction. Later, but still in an algebraic geometry spirit, many general methods were developed (e.g., see the papers of Hochschild, Mostow, Rosenlicht et al.).


Homogeneous Space Algebraic Group Maximal Compact Subgroup Open Orbit Homogeneous Manifold 
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Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • A. T. Huckleberry
    • 1
  • E. Oeljeklaus
    • 2
  1. 1.Fachbereich MathematikUniversität BochumBochumGermany
  2. 2.Fachbereich MathematikUniversität BremenBremen 33Germany

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