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Effective Actions of the Unitary Group on Complex Manifolds

  • A. V. Isaev (a1) and N. G. Kruzhilin (a2)
Abstract

We classify all connected n-dimensional complex manifolds admitting effective actions of the unitary group Un by biholomorphic transformations. One consequence of this classification is a characterization of by its automorphism group.

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References
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[A1] Akhiezer, D. N., On the homotopy classification of complex homogeneous spaces (translated from Russian). Trans. Moscow Math. Soc. 35 (1979), 119.
[A2] Akhiezer, D. N., Homogeneous complex manifolds (translated from Russian). Encyclopaedia Math. Sci. 10, Several Complex Variables IV, 1990, 195244, Springer-Verlag.
[AL] Andersen, E. and Lempert, L., On the group of holomorphic automorphisms of Cn . Invent.Math. 110 (1992), 371388.
[GG] Goto, M. and Grosshans, F., Semisimple Lie Algebras. Marcel Dekker, 1978.
[H] Hochschild, G., The Structure of Lie groups. Holden-Day, 1965.
[IKra] Isaev, A. V. and Krantz, S. G., On the automorphism groups of hyperbolic manifolds. J. Reine Angew.Math. 534 (2001), 187194.
[K] Kaup, W., Reelle Transformationsgruppen und invariante Metriken auf komplexen Räumen. Invent.Math. 3 (1967), 4370.
[R] Rossi, H., Attaching analytic spaces to an analytic space along a pseudoconcave boundary. Proc. Conf. Complex Analysis, Minneapolis, 1964, Springer-Verlag, 1965, 242256.
[VO] Vinberg, E. and Onishchik, A., Lie Groups and Algebraic Groups. Springer-Verlag, 1990.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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