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Article: Analytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogeneous manifolds
Title  Analytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogeneous manifolds 

Authors  
Issue Date  2010 
Publisher  Lehigh University, Dept of Mathematics. The Journal's web site is located at http://www.lehigh.edu/~math/jdg.html 
Citation  Journal Of Differential Geometry, 2010, v. 86 n. 3, p. 539567 How to Cite? 
Abstract  In a series of works, one of the authors has developed with J.M. Hwang a geometric theory of uniruled projective manifolds, especially those of Picard number 1, basing on the study of varieties of minimal rational tangents. A fundamental result in this theory is a principle of analytic continuation under very mild assumptions, called CartanFubini extension, of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents. In this article we develop a generalization of CartanFubini extension for nonequidimensional holomorphic immersions from a connected open subset of a Fano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends varieties of minimal rational tangents onto linear sections of varieties of minimal rational tangents and that it satisfies a mild geometric condition formulated in terms of second fundamental forms on varieties of minimal rational tangents. Formerly such a result was known only in the very special case of irreducible Hermitian symmetric manifolds of rank at least two, and the proof relied on the existence of flattening coordinates, viz., HarishChandra coordinates, with respect to which the varieties of minimal rational tangents form a constant family. The proof of the main result, which is based on the deformation theory of rational curves, is differentialgeometric in nature and is applicable to the general situation of uniruled projective manifolds without any assumption on the existence of special coordinate systems. As an application, we give a characterization of standard embeddings for certain pairs of rational homogeneous manifolds in terms of embeddings of varieties of minimal rational tangents. 
Persistent Identifier  http://hdl.handle.net/10722/135148 
ISSN  2017 Impact Factor: 1.562 2015 SCImago Journal Rankings: 3.244 
References 
DC Field  Value  Language 

dc.contributor.author  Hong, J  en_HK 
dc.contributor.author  Mok, N  en_HK 
dc.date.accessioned  20110727T01:29:07Z   
dc.date.available  20110727T01:29:07Z   
dc.date.issued  2010  en_HK 
dc.identifier.citation  Journal Of Differential Geometry, 2010, v. 86 n. 3, p. 539567  en_HK 
dc.identifier.issn  0022040X  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/135148   
dc.description.abstract  In a series of works, one of the authors has developed with J.M. Hwang a geometric theory of uniruled projective manifolds, especially those of Picard number 1, basing on the study of varieties of minimal rational tangents. A fundamental result in this theory is a principle of analytic continuation under very mild assumptions, called CartanFubini extension, of biholomorphisms between connected open subsets of two Fano manifolds of Picard number 1 which preserve varieties of minimal rational tangents. In this article we develop a generalization of CartanFubini extension for nonequidimensional holomorphic immersions from a connected open subset of a Fano manifold of Picard number 1 into a uniruled projective manifold, under the assumptions that the map sends varieties of minimal rational tangents onto linear sections of varieties of minimal rational tangents and that it satisfies a mild geometric condition formulated in terms of second fundamental forms on varieties of minimal rational tangents. Formerly such a result was known only in the very special case of irreducible Hermitian symmetric manifolds of rank at least two, and the proof relied on the existence of flattening coordinates, viz., HarishChandra coordinates, with respect to which the varieties of minimal rational tangents form a constant family. The proof of the main result, which is based on the deformation theory of rational curves, is differentialgeometric in nature and is applicable to the general situation of uniruled projective manifolds without any assumption on the existence of special coordinate systems. As an application, we give a characterization of standard embeddings for certain pairs of rational homogeneous manifolds in terms of embeddings of varieties of minimal rational tangents.  en_HK 
dc.language  eng  en_US 
dc.publisher  Lehigh University, Dept of Mathematics. The Journal's web site is located at http://www.lehigh.edu/~math/jdg.html  en_HK 
dc.relation.ispartof  Journal of Differential Geometry  en_HK 
dc.title  Analytic continuation of holomorphic maps respecting varieties of minimal rational tangents and applications to rational homogeneous manifolds  en_HK 
dc.type  Article  en_HK 
dc.identifier.email  Mok, N:nmok@hkucc.hku.hk  en_HK 
dc.identifier.authority  Mok, N=rp00763  en_HK 
dc.description.nature  link_to_subscribed_fulltext   
dc.identifier.scopus  eid_2s2.079953323687  en_HK 
dc.identifier.hkuros  186042  en_US 
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.079953323687&selection=ref&src=s&origin=recordpage  en_HK 
dc.identifier.volume  86  en_HK 
dc.identifier.issue  3  en_HK 
dc.identifier.spage  539  en_HK 
dc.identifier.epage  567  en_HK 
dc.publisher.place  United States  en_HK 
dc.identifier.scopusauthorid  Hong, J=15750365300  en_HK 
dc.identifier.scopusauthorid  Mok, N=7004348032  en_HK 