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Article: Characterization of certain holomorphic geodesic cycles on quotients of bounded symmetric domains in terms of tangent subspaces

TitleCharacterization of certain holomorphic geodesic cycles on quotients of bounded symmetric domains in terms of tangent subspaces
Authors
KeywordsBounded symmetric domains
Characteristic bundles
Complex Finsler metrics
Geodesic cycles
Holomorphic mappings
Issue Date2002
PublisherLondon Mathematical Society. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=COM
Citation
Compositio Mathematica, 2002, v. 132 n. 3, p. 289-309 How to Cite?
AbstractLet Ω be an irreducible bounded symmetric domain and Γ ⊂ Aut(Ω) be a torsion-free discrete group of automorphisms, X:= Ω/Γ. We study the problem of algebro-geometric and differential-geometric characterizations of certain compact holomorphic geodesic cycles S ⊂ X. We treat special cases of the problem, pertaining to a situation in which S is a compact holomorphic curve, and to the case where Ω is a classical domain dual to the hyperquadric. In both cases we consider algebro-geometric characterizations in terms of tangent subspaces. As a consequence we derive effective pinching theorems where certain complex submanifolds S ⊂ X are proven to be totally geodesic whenever their scalar curvatures are pinched between certain computed universal constants, independent of the volume of the submanifold S, giving new examples of the gap phenomenon for the characterization of compact holomorphic geodesic cycles.
Persistent Identifierhttp://hdl.handle.net/10722/42124
ISSN
2015 Impact Factor: 1.069
2015 SCImago Journal Rankings: 2.965
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorMok, Nen_HK
dc.date.accessioned2007-01-08T02:29:40Z-
dc.date.available2007-01-08T02:29:40Z-
dc.date.issued2002en_HK
dc.identifier.citationCompositio Mathematica, 2002, v. 132 n. 3, p. 289-309en_HK
dc.identifier.issn0010-437Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/42124-
dc.description.abstractLet Ω be an irreducible bounded symmetric domain and Γ ⊂ Aut(Ω) be a torsion-free discrete group of automorphisms, X:= Ω/Γ. We study the problem of algebro-geometric and differential-geometric characterizations of certain compact holomorphic geodesic cycles S ⊂ X. We treat special cases of the problem, pertaining to a situation in which S is a compact holomorphic curve, and to the case where Ω is a classical domain dual to the hyperquadric. In both cases we consider algebro-geometric characterizations in terms of tangent subspaces. As a consequence we derive effective pinching theorems where certain complex submanifolds S ⊂ X are proven to be totally geodesic whenever their scalar curvatures are pinched between certain computed universal constants, independent of the volume of the submanifold S, giving new examples of the gap phenomenon for the characterization of compact holomorphic geodesic cycles.en_HK
dc.format.extent214705 bytes-
dc.format.extent26624 bytes-
dc.format.extent766772 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/msword-
dc.format.mimetypeapplication/pdf-
dc.languageengen_HK
dc.publisherLondon Mathematical Society. The Journal's web site is located at http://journals.cambridge.org/action/displayJournal?jid=COMen_HK
dc.relation.ispartofCompositio Mathematicaen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rightsCompositio Mathematica. Copyright © London Mathematical Society.en_HK
dc.subjectBounded symmetric domainsen_HK
dc.subjectCharacteristic bundlesen_HK
dc.subjectComplex Finsler metricsen_HK
dc.subjectGeodesic cyclesen_HK
dc.subjectHolomorphic mappingsen_HK
dc.titleCharacterization of certain holomorphic geodesic cycles on quotients of bounded symmetric domains in terms of tangent subspacesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0010-437X&volume=132&issue=3&spage=289&epage=309&date=2002&atitle=Characterization+of+Certain+Holomorphic+Geodesic+Cycles+on+Quotients+of+Bounded+Symmetric+Domains+in+terms+of+Tangent+Subspacesen_HK
dc.identifier.emailMok, N:nmok@hkucc.hku.hken_HK
dc.identifier.authorityMok, N=rp00763en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1023/A:1016505024858en_HK
dc.identifier.scopuseid_2-s2.0-0036321478en_HK
dc.identifier.hkuros66703-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0036321478&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume132en_HK
dc.identifier.issue3en_HK
dc.identifier.spage289en_HK
dc.identifier.epage309en_HK
dc.identifier.isiWOS:000177100300003-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridMok, N=7004348032en_HK

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