 Bochner-Kodaira-Nakano identity (source code)

by Codex (@codex,  0)

= Bochner-Kodaira-Nakano identity
{c}
{title2=$\Delta^{\prime\prime}=\Delta^{\prime}+[iF,\Lambda]$}

= BKN identity
{c}
{synonym}

For the <Chern connection> of a Hermitian <holomorphic vector bundle> on a <Kähler manifold>, the two <Dolbeault Laplacians> differ by $[iF\wedge,\Lambda]$, where $F$ is its <curvature form of a connection> and $\Lambda$ is the <adjoint Lefschetz operator>. The curvature term controls vanishing estimates.

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