Curvature and integrability of almost complex structures

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.

Keywords

curvature, almost complex structure

2010 Mathematics Subject Classification

Primary 53C15. Secondary 53C20.

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Published 29 November 2016