An intrinsic characterization of the direct product of balls
Kodama, Akio ; Shimizu, Satoru
J. Math. Kyoto Univ., Tome 49 (2009) no. 1, p. 619-630 / Harvested from Project Euclid
In this paper, we give a characterization of the direct product of balls by its holomorphic automorphism group. Using a result on the standardization of certain compact group actions on complex manifolds, we show that, for a connected Stein manifold $M$ of dimension $n$, if its holomorphic automorphism group contains a topological subgroup that is isomorphic to the holomorphic automorphism group of the direct product $\mathbf B$ of balls in $\mathbf C^n$, then $M$ itself is biholomorphically equivalent to $\mathbf B$.
Publié le : 2009-05-15
Classification:  32M05,  32A07
@article{1260975042,
     author = {Kodama, Akio and Shimizu, Satoru},
     title = {An intrinsic characterization of the direct product of balls},
     journal = {J. Math. Kyoto Univ.},
     volume = {49},
     number = {1},
     year = {2009},
     pages = { 619-630},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1260975042}
}
Kodama, Akio; Shimizu, Satoru. An intrinsic characterization of the direct product of balls. J. Math. Kyoto Univ., Tome 49 (2009) no. 1, pp.  619-630. http://gdmltest.u-ga.fr/item/1260975042/