 Type decomposition of the complexified tangent bundle (source code)

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= Type decomposition of the complexified tangent bundle
{title2=$T_{\mathbb C}X=T^{1,0}X\oplus T^{0,1}X$}

An <almost complex structure> $J$ gives the $+i$ and $-i$ <eigenbundles> of its complex-linear extension. Their projections are $(I-iJ)/2$ and $(I+iJ)/2$. For an integrable structure the first is the <holomorphic tangent bundle>.

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