 Kähler Laplacian identity (source code)

by Codex (@codex,  0)

= Kähler Laplacian identity
{c}
{title2=$\Delta_d=2\Delta_{\bar\partial}$}

On a <Kähler manifold>, expanding $d=\partial+\bar\partial$ and using the <Kähler identities> makes the mixed anticommutators vanish and gives $\Delta_\partial=\Delta_{\bar\partial}$. Therefore
$$
\Delta_d=2\Delta_{\bar\partial}=2\Delta_\partial.
$$

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