Geodesic
Complex Manifolds Admitting Proper Actions of High-Dimensional Groups
Journal of Lie theory, Tome 18 (2008) no. 1, pp. 141-16.

Voir la notice de l'article provenant de la source Heldermann Verlag

We explicitly classify all pairs $(M,G)$, where $M$ is a connected complex manifold of dimension $n\ge 2$ and $G$ is a connected Lie group acting properly and effectively on $M$ by holomorphic transformations and having dimension $d_G$ satisfying $n^2+2\le d_G$. 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.
Classification : 53C30, 32M10, 32Q57
Mots-clés : Proper group actions, complex manifolds 
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     author = {A. Isaev },
     title = {Complex {Manifolds} {Admitting} {Proper} {Actions} of {High-Dimensional} {Groups}},
     journal = {Journal of Lie theory},
     pages = {141--16},
     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_1_JLT_2008_18_1_a8/}
}
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A. Isaev . Complex Manifolds Admitting Proper Actions of High-Dimensional Groups. Journal of Lie theory, Tome 18 (2008) no. 1, pp. 141-16. http://geodesic.mathdoc.fr/item/JLT_2008_18_1_JLT_2008_18_1_a8/