TY - JOUR
T1 - Effective Transitive Actions of the Unitary Group on Quotients of Hopf Manifolds
AU - Isaev, Alexander
N1 - Publisher Copyright:
© 2016, Mathematica Josephina, Inc.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - In our joint article with N. Kruzhilin of 2002, we showed that every connected complex manifold of dimension n≥ 2 that admits an effective transitive action by holomorphic transformations of the unitary group U n is biholomorphic to the quotient of a Hopf manifold by the action of Zm for some integer m satisfying (n, m) = 1. In this note, we complement the above result with an explicit description of all effective transitive actions of U n on such quotients, which provides an answer to a 10-year-old question.
AB - In our joint article with N. Kruzhilin of 2002, we showed that every connected complex manifold of dimension n≥ 2 that admits an effective transitive action by holomorphic transformations of the unitary group U n is biholomorphic to the quotient of a Hopf manifold by the action of Zm for some integer m satisfying (n, m) = 1. In this note, we complement the above result with an explicit description of all effective transitive actions of U n on such quotients, which provides an answer to a 10-year-old question.
KW - Hopf manifolds
KW - Transitive group actions
UR - http://www.scopus.com/inward/record.url?scp=84988592570&partnerID=8YFLogxK
U2 - 10.1007/s12220-016-9744-5
DO - 10.1007/s12220-016-9744-5
M3 - Article
SN - 1050-6926
VL - 27
SP - 1914
EP - 1919
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 3
ER -