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- W2892901140 abstract "We study holomorphic Legendrian curves in the standard complex contact structure on the projectivised cotangent bundle $X=mathbb P(T^*Z)$ of a complex manifold $Z$ of dimension at least $2$. We 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 $Mto X$ 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 $X$." @default.
- W2892901140 created "2018-10-05" @default.
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- W2892901140 date "2022-01-01" @default.
- W2892901140 modified "2023-09-23" @default.
- W2892901140 title "Holomorphic Legendrian curves in projectivised cotangent bundles" @default.
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- W2892901140 doi "https://doi.org/10.1512/iumj.2022.71.8767" @default.
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