Curvature and integrability of almost complex structures
arXiv:1501.00629
Abstract
This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the complex structures on an almost complex manifold. I also discuss the almost-Hermitian case of harmonic complex structures and the connections with balanced structures.
arXiv commentto appear in Pure and Applied Mathematics Quarterly