Timeline for Integrability of an almost complex structure vs holomorphicity of the section $M\rightarrow \mathcal{J}(M)$
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Dec 8, 2018 at 5:26 | comment | added | rori | but if $M$ is an open ball with a fixed embedding to $\mathbb{R}^{2n}$, then the restriction of Levi--Civita connection from $\mathbb{R}^{2n}$ provides us with a flat connection on $TM$. Do we get a complex structure on the total space of the bundle? | |
| Dec 8, 2018 at 1:50 | comment | added | Qfwfq | (A minor remark: the bundle with fiber $\mathrm{SO}(2n)/\mathrm{U}(n)$ parametrizes almost complex structures which are orthogonal with respect to a given Riemanniann metric and preserve a given orientation on $M$, rather then all almost complex structures) | |
| Dec 7, 2018 at 21:26 | history | answered | gulag57 | CC BY-SA 4.0 |