Holomorphic Legendrian Curves in Projectivised Cotangent Bundles

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dc.contributor.authorForstneric, F.
dc.contributor.authorLarusson, F.
dc.date.issued2022
dc.description.abstractWe 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.statementofresponsibilityForstneric, Franc, Larusson, Finnur
dc.identifier.citationIndiana University Mathematics Journal, 2022; 71(1):93-124
dc.identifier.doi10.1512/iumj.2022.71.8767
dc.identifier.issn0022-2518
dc.identifier.issn1943-5258
dc.identifier.orcidLarusson, F. [0000-0001-5691-4942]
dc.identifier.urihttps://hdl.handle.net/2440/134745
dc.language.isoen
dc.publisherIndiana University Mathematics Journal
dc.relation.granthttp://purl.org/au-research/grants/arc/DP150103442
dc.rights©2022 Indiana University Mathematics Journal
dc.source.urihttps://iumj.org/
dc.subjectComplex contact manifold; projectivised cotangent bundle; Legendrian curve; Riemann surface; Stein manifold; Oka principle; h-principle
dc.titleHolomorphic Legendrian Curves in Projectivised Cotangent Bundles
dc.typeJournal article
pubs.publication-statusPublished

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