An Integrability Theorem for Almost-K\"ahler Structures using J-anti-invariant Two-Forms on Four-Manifolds
Differential Geometry
2015-09-04 v2 Complex Variables
Symplectic Geometry
Abstract
We establish a new criterion for a compatible almost complex structure on a symplectic four-manifold to be integrable and hence K\"ahler. Our main theorem shows that the existence of three linearly independent closed J-anti-invariant two-forms implies the integrability of the almost complex structure. This proves the conjecture of Draghici-Li-Zhang in the almost-K\"ahler case
Keywords
Cite
@article{arxiv.1507.00282,
title = {An Integrability Theorem for Almost-K\"ahler Structures using J-anti-invariant Two-Forms on Four-Manifolds},
author = {Mehdi Lejmi and Markus Upmeier},
journal= {arXiv preprint arXiv:1507.00282},
year = {2015}
}
Comments
This paper has been withdrawn due to a crucial sign error in the proof of Proposition 14. The authors are very thankful to Tedi Draghici for kindly pointing it out