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Nov 16, 2019 at 13:36 comment added Ben McKay Since $E$ is trivial on $N$ and $F$ is trivial on $N$, if they are isomorphic, they are both trivial, so $M$ and $N$ have trivial tangent bundle. It then follows that there is an almost complex structure. For example, any 3-manifolds $M$ and $N$ have trivial tangent bundle, so the resulting $M \times N$ has an almost complex structure with two totally real fibrations.
Nov 16, 2019 at 1:55 comment added liding Thank you!Thank you!
Nov 15, 2019 at 21:58 history undeleted DamienC
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Nov 15, 2019 at 21:25 history deleted DamienC via Vote
Nov 15, 2019 at 21:13 history answered DamienC CC BY-SA 4.0