The study reveals properties of almost complex structures in compact manifolds, suggesting key insights for their classification.
Using the existence of real analytic curves of almost complex structures, we prove that, on a compact almost complex manifold, the space of almost complex structures whose Nijenhuis tensor has rank at least k at every point is either open and dense or empty in each path-connected component of the space of almost complex structures. In particular, our result holds for maximally non-integrable almost complex structures.
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Lorenzo Sillari (2026) studied this question.
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