On proper actions of Lie groups of dimension n2+1 on n-dimensional complex manifolds
Abstract
We explicitly classify all pairs (M,G), where M is a connected complex manifold of dimension n[greater-or-equal, slanted]2 and G is a connected Lie group acting properly and effectively on M by holomorphic transformations and having dimension dG satisfying n2+2[less-than-or-equals, slant]dG<n2+2n. We also consider the case dG=n2+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 n2+2n and generalize some of the author's earlier work on Kobayashi-hyperbolic manifolds with high-dimensional holomorphic automorphism group.
- Publication:
-
Journal of Mathematical Analysis and Applications
- Pub Date:
- June 2008
- DOI:
- 10.1016/j.jmaa.2007.12.050
- arXiv:
- arXiv:0711.2098
- Bibcode:
- 2008JMAA..342.1160I
- Keywords:
-
- Complex manifolds;
- Proper group actions;
- Mathematics - Complex Variables;
- Mathematics - Differential Geometry;
- 32Q57;
- 32M10;
- 58D19
- E-Print:
- 60 pages