Agler, J, Lykova, Z and Young, NJ orcid.org/0000-0003-2707-1450 (2019) A geometric characterization of the symmetrized bidisc. Journal of Mathematical Analysis and Applications, 473 (2). pp. 1377-1413. ISSN 0022-247X
Abstract
The symmetrized bidisc
G def = {(z + w, zw) : |z| < 1, |w| < 1}
has interesting geometric properties. While it has a plentiful supply of complex geodesics and of automorphisms, there is nevertheless a unique complex geodesic in G that is invariant under all automorphisms of G. Moreover, G is foliated by those complex geodesics that meet in one point and have nontrivial stabilizer. We prove that these properties, together with two further geometric hypotheses on the action of the automorphism group of G, characterize the symmetrized bidisc in the class of complex manifolds.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 Elsevier Inc. All rights reserved. This is an author produced version of a paper published in Journal of Mathematical Analysis and Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Complex manifold; Geodesic; Automorphism; Cohomogeneity one |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number Newcastle University/EPSRC BH 122321 |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Jan 2019 11:57 |
Last Modified: | 16 Jan 2020 01:39 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jmaa.2019.01.027 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:140903 |