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

Abstract

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 contact structures are not globally contactomorphic to the standard complex contact structure on ${\mathbb{C}}^{2n+1}$.

to appear in J. Geom. Anal

References in corpus (1)

• Holomorphic Legendrian curves

Cited by in corpus (5)

• Holomorphic Legendrian curves
• Darboux charts around holomorphic Legendrian curves and applications
• The Calabi-Yau property of superminimal surfaces in self-dual Einstein four-manifolds
• Mergelyan approximation theorem for holomorphic Legendrian curves
• The Oka principle for holomorphic Legendrian curves in ${\mathbb{C}}^{2n+1}$