Forstneric, F.Larusson, F.2022-04-012022-04-012022Indiana University Mathematics Journal, 2022; 71(1):93-1240022-25181943-5258https://hdl.handle.net/2440/134745We 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.en©2022 Indiana University Mathematics JournalComplex contact manifold; projectivised cotangent bundle; Legendrian curve; Riemann surface; Stein manifold; Oka principle; h-principleJournal article10.1512/iumj.2022.71.87672022-04-01439067Larusson, F. [0000-0001-5691-4942]