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Several Complex Variables IV pp 195–244Cite as

Homogeneous Complex Manifolds

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Part of the book series: Encyclopaedia of Mathematical Sciences ((EMS,volume 10))

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.

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Notes

  1. 1.

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  1. D. N. Akhiezer
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  1. A.N. Belozersky Laboratory of Molecular Biology and Bioorganic Chemistry, Moscow State University, GSP-234, 119899, Moscow, USSR

    S. G. Gindikin

  2. Academy of Sciences of the USSR, Central Economic and Mathematical Institute, ul. Krasikova 32, 117418, Moscow, USSR

    G. M. Khenkin

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Akhiezer, D.N. (1990). Homogeneous Complex Manifolds. In: Gindikin, S.G., Khenkin, G.M. (eds) Several Complex Variables IV. Encyclopaedia of Mathematical Sciences, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61263-3_4

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  • DOI: https://doi.org/10.1007/978-3-642-61263-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64766-6

  • Online ISBN: 978-3-642-61263-3

  • eBook Packages: Springer Book Archive

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