Pure and Applied Mathematics Quarterly
Volume 11 (2015)
Curvature and integrability of almost complex structures
Pages: 491 – 502
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.
curvature, almost complex structure
2010 Mathematics Subject Classification
Primary 53C15. Secondary 53C20.