On proper actions of Lie groups of dimension n2+1 on n-dimensional complex manifolds

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:342

Article

Isaev, A. V.

关键词: complex manifolds;    proper group actions;   

DOI  :  10.1016/j.jmaa.2007.12.050

来源: Elsevier

【 摘 要 】

We explicitly classify all pairs (M, G), where M is a connected complex manifold of dimension n >= 2 and G is a connected Lie group acting properly and effectively on M by holomorphic transformations and having dimension d(G) satisfying n(2) + 2 <= d(G) < n(2) + 2n. We also consider the case d(G) = n(2) + 1. In this case all actions split into three types according to the form of the linear isotropy subgroup. We give a complete explicit description of all pairs (M, G) for two of these types, as well as a large number of examples of actions of the third type. These results complement a theorem due to W. Kaup for the maximal group dimension n(2) + 2n and generalize some of the author's earlier work on Kobayashi-hyperbolic manifolds with high-dimensional holomorphic automorphism group. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free