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|Title:||Holomorphic Legendrian Curves in Projectivised Cotangent Bundles|
|Citation:||Indiana University Mathematics Journal, 2022; 71(1):93-124|
|Publisher:||Indiana University Mathematics Journal|
|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|
|Appears in Collections:||Mathematical Sciences publications|
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