We give several explicit examples of compact manifolds with a 1-parameter family of almost complex structures having arbitrarily small Nijenhuis tensor in the C0-norm. The 4-dimensional examples possess no complex structure, whereas the 6-dimensional example does not possess a left invariant complex structure, and whether it possesses a complex structure appears to be unknown.
 T. Fei, D. Phong, S. Picard, and X. Zhang. Geometric flows for the type IIA string. Preprint arxiv:2011.03662v1, 2020.Search in Google Scholar
 A. Hattori. Spectral sequence in the de Rham cohomology of fibre bundles. J. Fac. Sci. Univ. Tokyo Sect. I, 8:289–331 (1960), 1960.Search in Google Scholar
 A. I. Mal’cev. On a class of homogeneous spaces. Izvestiya Akad. Nauk. SSSR. Ser. Mat. Amer. Math. Soc. Transl., 39 (1951), 13:9–32, 1949.Search in Google Scholar
 Aleksandar Milivojević. On the realization of symplectic algebras and rational homotopy types by closed symplectic manifolds. Proc. Amer. Math. Soc., 149(5):2257–2263, 2021.10.1090/proc/15397Search in Google Scholar
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