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Oct 7, 2020 at 12:37 vote accept CommunityBot
Oct 7, 2020 at 12:28 comment added Dmitri Panov Because you can choose an almost complex structure in a ball as you wish, and then extend to the whole manifold. Basically, when you have some almost complex structure on your manifold, you can take a point $p$ and a very small neighbourhood of it with some smooth coordinates. Then in this small neighbourhood $J$ is almost constant. You can perturb it to make it constant
Oct 7, 2020 at 12:16 comment added user164740 why is there an almost complex structure that is integrable in some closed ball?
Oct 7, 2020 at 11:56 history answered Dmitri Panov CC BY-SA 4.0