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https://hdl.handle.net/2440/134745
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DC Field | Value | Language |
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dc.contributor.author | Forstneric, F. | - |
dc.contributor.author | Larusson, F. | - |
dc.date.issued | 2022 | - |
dc.identifier.citation | Indiana University Mathematics Journal, 2022; 71(1):93-124 | - |
dc.identifier.issn | 0022-2518 | - |
dc.identifier.issn | 1943-5258 | - |
dc.identifier.uri | https://hdl.handle.net/2440/134745 | - |
dc.description.abstract | We study holomorphic Legendrian curves in the standard complex contact structure on the projectivised cotangent bunWe provide a detailed analysis of Legendrian curves degenerating to vertical curves and obtain several approximation and general position theorems. In particular, we prove that any vertical holomorphic curve M -> X from a compact bordered Riemann surface M can be deformed to a horizontal Legendrian curve by an arbitrarily small deformation. A similar result is proved in the parametric setting, provided that all vertical curves under consideration are nondegenerate. Stronger results are obtained when the base Z is an Oka manifold or a Stein manifold with the density property. Finally, we establish basic and 1-parametric h-principles for holomorphic Legendrian curves in X. | - |
dc.description.statementofresponsibility | Forstneric, Franc, Larusson, Finnur | - |
dc.language.iso | en | - |
dc.publisher | Indiana University Mathematics Journal | - |
dc.rights | ©2022 Indiana University Mathematics Journal | - |
dc.source.uri | https://iumj.org/ | - |
dc.subject | Complex contact manifold; projectivised cotangent bundle; Legendrian curve; Riemann surface; Stein manifold; Oka principle; h-principle | - |
dc.title | Holomorphic Legendrian Curves in Projectivised Cotangent Bundles | - |
dc.type | Journal article | - |
dc.identifier.doi | 10.1512/iumj.2022.71.8767 | - |
dc.relation.grant | http://purl.org/au-research/grants/arc/DP150103442 | - |
pubs.publication-status | Published | - |
dc.identifier.orcid | Larusson, F. [0000-0001-5691-4942] | - |
Appears in Collections: | Mathematical Sciences publications |
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