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Type: Journal article
Title: Holomorphic Legendrian Curves in Projectivised Cotangent Bundles
Author: Forstneric, F.
Larusson, F.
Citation: Indiana University Mathematics Journal, 2022; 71(1):93-124
Publisher: Indiana University Mathematics Journal
Issue Date: 2022
ISSN: 0022-2518
Statement of
Forstneric, Franc, Larusson, Finnur
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.
Keywords: Complex contact manifold; projectivised cotangent bundle; Legendrian curve; Riemann surface; Stein manifold; Oka principle; h-principle
Rights: ©2022 Indiana University Mathematics Journal
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Appears in Collections:Mathematical Sciences publications

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