Answer by Misha Verbitsky for Which almost complex manifolds admit a complex...
In complex dimension 3 or more it is still an open conjecture(which was re-stated Yau a couple of years ago in his UCLA lectures).There is not a single known example of an almost complex manifoldof...
View ArticleAnswer by Francesco Polizzi for Which almost complex manifolds admit a...
There are actually counterexamples in real dimension $4$.The first examples of compact almost complex $4$-manifolds admitting no complex structure were produced by Van de Ven in his paper "On the Chern...
View ArticleWhich almost complex manifolds admit a complex structure?
I was reading Yau's list of problems in geometry, and one of them is to prove that any almost complex manifold of complex dimension $n \geq 3$ admits a complex structure. It's been some time since...
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