If $\nabla$ is a torsionfree connection and $(\nabla_{X}J)Y=(\nabla_{Y}J)X$, J- an almost complex structure, and $\nabla_{X}^{*}Y:=J\nabla_{X}(JY)$ its dual connecion. Is it correct to conclude that $[X,Y]=0$?
2026-03-25 23:35:52.1774481752
Dual connections, bracket
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