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$\begingroup$ LeBrun's comment appears in the paper Orthogonal Complex Structures on $S^6$. His reasoning is that by blowing up $S^6$, one would obtain a complex three-manifold diffeomorphic to $\mathbb{CP}^3$, but not biholomorphic to it. In fact, the resulting complex structure wouldn't even be Kähler! $\endgroup$

Michael Albanese
– Michael Albanese

2018-12-21 05:00:07 +00:00
Commented Dec 21, 2018 at 5:00
1

$\begingroup$ Re, Orthogonal complex structures on $S^6$. $\endgroup$

LSpice
– LSpice

2023-09-02 22:51:33 +00:00
Commented Sep 2, 2023 at 22:51

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