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Article: On the structure of holomorphic isometric embeddings of complex unit balls into bounded symmetric domains
Title | On the structure of holomorphic isometric embeddings of complex unit balls into bounded symmetric domains |
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Authors | |
Keywords | Bergman metrics holomorphic isometric embeddings bounded symmetric domains Borel embedding complex unit balls |
Issue Date | 2018 |
Publisher | Mathematical Sciences Publishers. The Journal's web site is located at http://msp.org/pjm/ |
Citation | Pacific Journal of Mathematics, 2018, v. 295 n. 2, p. 291-315 How to Cite? |
Abstract | We study general properties of holomorphic isometric embeddings of complex unit balls B(double-struck)n into bounded symmetric domains of rank ≥ 2. In the first part, we study holomorphic isometries from (B(double-struck)n, kgB(double-struck)n) to (Ω, gΩ) with nonminimal isometric constants k for any irreducible bounded symmetric domain Ω of rank ≥ 2, where gD denotes the canonical Kähler-Einstein metric on any irreducible bounded symmetric domain D normalized so that minimal disks of D are of constant Gaussian curvature -2. In particular, results concerning the upper bound of the dimension of isometrically embedded B(double-struck)n in Ω and the structure of the images of such holomorphic isometries are obtained. In the second part, we study holomorphic isometries from (B(double-struck)n, gB(double-struck)n ) to (Ω, gΩ) for any irreducible bounded symmetric domains Ω (double subset) N of rank equal to 2 with 2N > N'+1, where N' is an integer such that ℓ: Xc, (right arrow, hooked)N' is the minimal embedding (i.e., the first canonical embedding) of the compact dual Hermitian symmetric space Xc of Ω. We completely classify images of all holomorphic isometries from (B(double-struck)n, gB(double-struck)n ) to (Ω, gΩ) for 1 ≤ n ≤ n0(Ω), where n0(Ω):=: 2N - N' > 1. In particular, for 1 ≤ n ≤ n0(Ω)-1 we prove that any holomorphic isometry from (B(double-struck)n, gB(double-struck)n ) to (Ω, gΩ) extends to some holomorphic isometry from (B(double-struck)n0(Ω), gB(double-struck)n0(Ω) to (Ω, gΩ). © 2018 Mathematical Sciences Publishers. |
Persistent Identifier | http://hdl.handle.net/10722/272212 |
ISSN | 2021 Impact Factor: 0.648 2020 SCImago Journal Rankings: 0.967 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Chan, ST | - |
dc.date.accessioned | 2019-07-20T10:37:52Z | - |
dc.date.available | 2019-07-20T10:37:52Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Pacific Journal of Mathematics, 2018, v. 295 n. 2, p. 291-315 | - |
dc.identifier.issn | 0030-8730 | - |
dc.identifier.uri | http://hdl.handle.net/10722/272212 | - |
dc.description.abstract | We study general properties of holomorphic isometric embeddings of complex unit balls B(double-struck)n into bounded symmetric domains of rank ≥ 2. In the first part, we study holomorphic isometries from (B(double-struck)n, kgB(double-struck)n) to (Ω, gΩ) with nonminimal isometric constants k for any irreducible bounded symmetric domain Ω of rank ≥ 2, where gD denotes the canonical Kähler-Einstein metric on any irreducible bounded symmetric domain D normalized so that minimal disks of D are of constant Gaussian curvature -2. In particular, results concerning the upper bound of the dimension of isometrically embedded B(double-struck)n in Ω and the structure of the images of such holomorphic isometries are obtained. In the second part, we study holomorphic isometries from (B(double-struck)n, gB(double-struck)n ) to (Ω, gΩ) for any irreducible bounded symmetric domains Ω (double subset) N of rank equal to 2 with 2N > N'+1, where N' is an integer such that ℓ: Xc, (right arrow, hooked)N' is the minimal embedding (i.e., the first canonical embedding) of the compact dual Hermitian symmetric space Xc of Ω. We completely classify images of all holomorphic isometries from (B(double-struck)n, gB(double-struck)n ) to (Ω, gΩ) for 1 ≤ n ≤ n0(Ω), where n0(Ω):=: 2N - N' > 1. In particular, for 1 ≤ n ≤ n0(Ω)-1 we prove that any holomorphic isometry from (B(double-struck)n, gB(double-struck)n ) to (Ω, gΩ) extends to some holomorphic isometry from (B(double-struck)n0(Ω), gB(double-struck)n0(Ω) to (Ω, gΩ). © 2018 Mathematical Sciences Publishers. | - |
dc.language | eng | - |
dc.publisher | Mathematical Sciences Publishers. The Journal's web site is located at http://msp.org/pjm/ | - |
dc.relation.ispartof | Pacific Journal of Mathematics | - |
dc.rights | ©2018 Mathematical Sciences Publishers. First published in Pacific Journal of Mathematics in Vol. 295 (2018), No. 2, published by Mathematical Sciences Publishers | - |
dc.subject | Bergman metrics | - |
dc.subject | holomorphic isometric embeddings | - |
dc.subject | bounded symmetric domains | - |
dc.subject | Borel embedding | - |
dc.subject | complex unit balls | - |
dc.title | On the structure of holomorphic isometric embeddings of complex unit balls into bounded symmetric domains | - |
dc.type | Article | - |
dc.identifier.email | Chan, ST: mastchan@hku.hk | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.2140/pjm.2018.295.291 | - |
dc.identifier.scopus | eid_2-s2.0-85045835279 | - |
dc.identifier.hkuros | 298634 | - |
dc.identifier.volume | 295 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 291 | - |
dc.identifier.epage | 315 | - |
dc.identifier.isi | WOS:000432891800003 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0030-8730 | - |