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Proper actions of lie groups of dimension n 2 + 1 on n-dimensional complex manifolds

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Abstract

In this paper, we continue to study actions of high-dimensional Lie groups on complex manifolds. We give a complete explicit description of all pairs (M,G), where M is a connected complex manifold of dimension n ≥ 2 and G is a connected Lie group of dimension n 2 +1 acting effectively and properly on M by holomorphic transformations. This result complements a classification obtained earlier by the first author for n 2 + 2 ≤ dimG < n 2 + 2n and a classical result due to W. Kaup for the maximal group dimension n 2 + 2n.

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Authors and Affiliations

  1. Department of Mathematics, The Australian National University, Canberra, ACT, 0200, Australia

    A. V. Isaev

  2. Department of Complex Analysis, Steklov Mathematical Institute, 8 Gubkina St., Moscow, GSP-1 119991, Russia

    N. G. Kruzhilin

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  1. A. V. Isaev
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  2. N. G. Kruzhilin
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Correspondence to A. V. Isaev.

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Isaev, A.V., Kruzhilin, N.G. Proper actions of lie groups of dimension n 2 + 1 on n-dimensional complex manifolds. Isr. J. Math. 172, 193–252 (2009). https://doi.org/10.1007/s11856-009-0071-4

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