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Sep 3, 2020 at 17:44 comment added Panagiotis Konstantis No, every closed, oriented $6$-manifold with vanishing third integer cohomology supports an almost complex structure.
Sep 3, 2020 at 17:42 comment added user164740 is there an easy way to rule out the existence of an almost complex or a complex structure on these manifolds?
Sep 3, 2020 at 17:40 history edited Panagiotis Konstantis CC BY-SA 4.0
Added edit.
Sep 3, 2020 at 17:15 comment added Jason Starr Are these manifolds the underlying topological manifolds of complex projective manifolds?
Sep 3, 2020 at 17:09 history answered Panagiotis Konstantis CC BY-SA 4.0