About integrability of almost complex structures on strictly Nearly K\"{a}hler 6-manifolds

TL;DR

This paper proves that on nearly Kähler 6-manifolds, any almost complex structure positively tamed by the symplectic form cannot be integrable, highlighting a fundamental geometric restriction.

Contribution

It establishes a non-integrability result for almost complex structures tamed by the symplectic form on nearly Kähler 6-manifolds, expanding understanding of their geometric properties.

Findings

Any positively tamed almost complex structure on such manifolds is not integrable.

The result constrains possible complex structures compatible with the nearly Kähler structure.

Supports the view that nearly Kähler 6-manifolds have rigid geometric structures.

Abstract

We show that any almost complex structure, positively tamed with $\omega$ on nearly K\"{a}hler 6-manifold $(M,g,J,\omega)$ is not integrable