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Article: On holomorphic immersions into Kahler manifolds of constant holomorphic sectional curvature
Title | On holomorphic immersions into Kahler manifolds of constant holomorphic sectional curvature |
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Authors | |
Keywords | Harmonic Form Holomorphic Splitting Second Fundamental Form Tangent Sequence Totally Geodesic Immersion |
Issue Date | 2005 |
Publisher | Science in China Press. The Journal's web site is located at http://www.scichina.com:8081/sciAe/EN/volumn/current.shtml |
Citation | Science In China, Series A: Mathematics, 2005, v. 48 SUPPL., p. 123-145 How to Cite? |
Abstract | We study holomorphic immersions f: X → M from a complex manifold X into a Kahler manifold of constant holomorphic sectional curvature M, i.e. a complex hyperbolic space form, a complex Euclidean space form, or the complex projective space equipped with the Fubini-Study metric. For X compact we show that the tangent sequence splits holomorphically if and only if f is a totally geodesic immersion. For X not necessarily compact we relate an intrinsic cohomological invariant p(x) on X, viz. the invariant defined by Gunning measuring the obstruction to the existence of holomorphic projective connections, to an extrinsic cohomological invariant v(f) measuring the obstruction to the holomorphic splitting of the tangent sequence. The two invariants p(X) and v(f) are related by a linear map on cohomology groups induced by the second fundamental form. In some cases, especially when X is a complex surface and M is of complex dimension 4, under the assumption that X admits a holomorphic projective connection we obtain a sufficient condition for the holomorphic splitting of the tangent sequence in terms of the second fundamental form. |
Persistent Identifier | http://hdl.handle.net/10722/156134 |
ISSN | 2011 Impact Factor: 0.701 |
References |
DC Field | Value | Language |
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dc.contributor.author | Mok, N | en_US |
dc.date.accessioned | 2012-08-08T08:40:32Z | - |
dc.date.available | 2012-08-08T08:40:32Z | - |
dc.date.issued | 2005 | en_US |
dc.identifier.citation | Science In China, Series A: Mathematics, 2005, v. 48 SUPPL., p. 123-145 | en_US |
dc.identifier.issn | 1006-9283 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156134 | - |
dc.description.abstract | We study holomorphic immersions f: X → M from a complex manifold X into a Kahler manifold of constant holomorphic sectional curvature M, i.e. a complex hyperbolic space form, a complex Euclidean space form, or the complex projective space equipped with the Fubini-Study metric. For X compact we show that the tangent sequence splits holomorphically if and only if f is a totally geodesic immersion. For X not necessarily compact we relate an intrinsic cohomological invariant p(x) on X, viz. the invariant defined by Gunning measuring the obstruction to the existence of holomorphic projective connections, to an extrinsic cohomological invariant v(f) measuring the obstruction to the holomorphic splitting of the tangent sequence. The two invariants p(X) and v(f) are related by a linear map on cohomology groups induced by the second fundamental form. In some cases, especially when X is a complex surface and M is of complex dimension 4, under the assumption that X admits a holomorphic projective connection we obtain a sufficient condition for the holomorphic splitting of the tangent sequence in terms of the second fundamental form. | en_US |
dc.language | eng | en_US |
dc.publisher | Science in China Press. The Journal's web site is located at http://www.scichina.com:8081/sciAe/EN/volumn/current.shtml | en_US |
dc.relation.ispartof | Science in China, Series A: Mathematics | en_US |
dc.subject | Harmonic Form | en_US |
dc.subject | Holomorphic Splitting | en_US |
dc.subject | Second Fundamental Form | en_US |
dc.subject | Tangent Sequence | en_US |
dc.subject | Totally Geodesic Immersion | en_US |
dc.title | On holomorphic immersions into Kahler manifolds of constant holomorphic sectional curvature | en_US |
dc.type | Article | en_US |
dc.identifier.email | Mok, N:nmok@hkucc.hku.hk | en_US |
dc.identifier.authority | Mok, N=rp00763 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1360/05za0008 | en_US |
dc.identifier.scopus | eid_2-s2.0-20444409513 | en_US |
dc.identifier.hkuros | 98234 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-20444409513&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 48 | en_US |
dc.identifier.issue | SUPPL. | en_US |
dc.identifier.spage | 123 | en_US |
dc.identifier.epage | 145 | en_US |
dc.publisher.place | China | en_US |
dc.identifier.scopusauthorid | Mok, N=7004348032 | en_US |