TY - JOUR
T1 - Addendum to our characterization of the unit polydisc
AU - Kodama, Akio
AU - Shimizu, Satoru
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2010
Y1 - 2010
N2 - In 2008, we obtained an intrinsic characterization of the unit polydisc Δn in Cn from the viewpoint of the holomorphic automorphism group. In connection with this, A. V. Isaev investigated the structure of a complex manifold M with the property that every isotropy subgroup of the holomorphic automorhism group of M is compact, and obtained the same characterization of Δn as ours among the class of all such manifolds. In this paper, we establish some extensions of these results. In particular, Isaev's characterization of the unit polydisc Δn is extended to that of any bounded symmetric domain in Cn.
AB - In 2008, we obtained an intrinsic characterization of the unit polydisc Δn in Cn from the viewpoint of the holomorphic automorphism group. In connection with this, A. V. Isaev investigated the structure of a complex manifold M with the property that every isotropy subgroup of the holomorphic automorhism group of M is compact, and obtained the same characterization of Δn as ours among the class of all such manifolds. In this paper, we establish some extensions of these results. In particular, Isaev's characterization of the unit polydisc Δn is extended to that of any bounded symmetric domain in Cn.
KW - Holomorphic automorphism groups
KW - Reinhardt domains
KW - Torus actions
KW - Unit polydisc
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U2 - 10.2996/kmj/1278076335
DO - 10.2996/kmj/1278076335
M3 - Article
AN - SCOPUS:77955188078
VL - 33
SP - 182
EP - 191
JO - Kodai Mathematical Journal
JF - Kodai Mathematical Journal
SN - 0386-5991
IS - 2
ER -