New constructions relating Real and Complex Contact Structure

Ali M. Elgindi

New constructions relating Real and Complex Contact Structure

辛几何 2026-06-25 v1 微分几何几何拓扑

作者: Ali M. Elgindi

摘要

We establish new connections between real and complex contact geometry via embeddings of 3-manifolds into $\C^3$ . We introduce a new \emph{contact wedge} construction combining two transverse real contact structures to make a new \emph{complex contact} structure, subject to obstructions measured by the Nijenhuis tensor and Dolbeault cohomology. Dually, we form a \emph{hedge} construction which extracts real contact structures from complex ones. Applying these tools, we prove that $\C^3$ admits uncountably many complex contact structures.

引用

@article{arxiv.2607.01264,
  title  = {New constructions relating Real and Complex Contact Structure},
  author = {Ali M. Elgindi},
  journal= {arXiv preprint arXiv:2607.01264},
  year   = {2026}
}