Pure and Applied Mathematics Quarterly

Volume 11 (2015)

Number 3

Curvature and integrability of almost complex structures

Pages: 491 – 502

DOI: https://dx.doi.org/10.4310/PAMQ.2015.v11.n3.a4


Jianming Wan (School of Mathematics, Northwest University, Xi’an, China)


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.

Published 29 November 2016