 Dolbeault partial connection (source code)

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= Dolbeault partial connection
{c}
{title2=$\bar\partial_E$}

A Dolbeault partial connection obeys $\bar\partial_E(fs)=\bar\partial f\otimes s+f\bar\partial_Es$. Its square is a tensorial $(0,2)$-form with values in $\operatorname{End}E$; it vanishes for the canonical partial connection of a holomorphic bundle.

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