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Article: On holomorphic isometric embeddings of the unit n-ball into products of two unit m-balls

TitleOn holomorphic isometric embeddings of the unit n-ball into products of two unit m-balls
Authors
KeywordsBergman metrics
Complex unit balls
Holomorphic isometric embeddings
Total geodesy
Issue Date2011
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00209/index.htm
Citation
Mathematische Zeitschrift, 2011, v. 268 n. 1-2, p. 347-354 How to Cite?
AbstractWe study holomorphic isometric embeddings of the complex unit n-ball into products of two complex unit m-balls with respect to their Bergman metrics up to normalization constants (the isometric constant). There are two trivial holomorphic isometric embeddings for m ≥ n, given by F1(z) = (0, In;m(z)) with the isometric constant equal to (m + 1)/(n + 1) and F2(z) = (In;m(z), In;m(z)) with the isometric constant equal to 2(m + 1)/(n + 1). Here In;m: ℂn → ℂm is the canonical embedding. We prove that when m < 2n, these are the only holomorphic isometric embeddings up to unitary transformations. © 2010 Springer-Verlag.
Persistent Identifierhttp://hdl.handle.net/10722/135153
ISSN
2015 Impact Factor: 0.674
2015 SCImago Journal Rankings: 1.483
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorNg, SCen_US
dc.date.accessioned2011-07-27T01:29:08Z-
dc.date.available2011-07-27T01:29:08Z-
dc.date.issued2011en_US
dc.identifier.citationMathematische Zeitschrift, 2011, v. 268 n. 1-2, p. 347-354en_US
dc.identifier.issn0025-5874-
dc.identifier.urihttp://hdl.handle.net/10722/135153-
dc.description.abstractWe study holomorphic isometric embeddings of the complex unit n-ball into products of two complex unit m-balls with respect to their Bergman metrics up to normalization constants (the isometric constant). There are two trivial holomorphic isometric embeddings for m ≥ n, given by F1(z) = (0, In;m(z)) with the isometric constant equal to (m + 1)/(n + 1) and F2(z) = (In;m(z), In;m(z)) with the isometric constant equal to 2(m + 1)/(n + 1). Here In;m: ℂn → ℂm is the canonical embedding. We prove that when m < 2n, these are the only holomorphic isometric embeddings up to unitary transformations. © 2010 Springer-Verlag.-
dc.languageengen_US
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00209/index.htmen_US
dc.relation.ispartofMathematische Zeitschriften_US
dc.rightsThe original publication is available at www.springerlink.comen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectBergman metrics-
dc.subjectComplex unit balls-
dc.subjectHolomorphic isometric embeddings-
dc.subjectTotal geodesy-
dc.titleOn holomorphic isometric embeddings of the unit n-ball into products of two unit m-ballsen_US
dc.typeArticleen_US
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0025-5874&volume=268&issue=1-2&spage=347&epage=354&date=2011&atitle=On+holomorphic+isometric+embeddings+of+the+unit+n-ball+into+products+of+two+unit+m-balls-
dc.identifier.emailNg, SC: h0008312@hkusua.hku.hken_US
dc.description.naturepostprint-
dc.identifier.doi10.1007/s00209-010-0675-8-
dc.identifier.scopuseid_2-s2.0-79955934377-
dc.identifier.hkuros186614en_US
dc.identifier.volume268en_US
dc.identifier.issue1-2en_US
dc.identifier.spage347en_US
dc.identifier.epage354en_US
dc.identifier.isiWOS:000290545000018-
dc.identifier.citeulike6788519-

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