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In this paper we construct complex contact structures on $\mathbb{C}^{2n+1}$for any $n\ge 1$ with the property that every holomorphic Legendrian map$\mathbb{C}\to \mathbb{C}^{2n+1}$ is constant. In particular, these contactstructures are not globally contactomorphic to the standard complex contactstructure on $\mathbb{C}^{2n+1}$.

Hyperbolic complex contact structures on $\mathbb{C}^{2n+1}$