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Homogeneous Spaces from a Complex Analytic Viewpoint

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Manifolds and Lie Groups

Part of the book series: Progress in Mathematics ((PM,volume 14))

Abstract

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.).

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Bochum, D-4630, Bochum, Germany

    A. T. Huckleberry

  2. Fachbereich Mathematik, Universität Bremen, D-2800, Bremen 33, Germany

    E. Oeljeklaus

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  1. A. T. Huckleberry
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  2. E. Oeljeklaus
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Editors and Affiliations

  1. Department of Mathematics, Washington University, St. Louis, Missouri, 63130, USA

    Jun-ichi Hano

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© 1981 Springer Science+Business Media New York

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Huckleberry, A.T., Oeljeklaus, E. (1981). Homogeneous Spaces from a Complex Analytic Viewpoint. In: Hano, Ji., Morimoto, A., Murakami, S., Okamoto, K., Ozeki, H. (eds) Manifolds and Lie Groups. Progress in Mathematics, vol 14. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-5987-9_8

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  • DOI: https://doi.org/10.1007/978-1-4612-5987-9_8

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-5989-3

  • Online ISBN: 978-1-4612-5987-9

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