Kähler metric
= Kähler metric
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{title2=$g_{i\bar j}=\partial_i\partial_{\bar j}K$}
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Locally, a Kähler metric is the complex Hessian $g_{i\bar j}=\partial_i\partial_{\bar j}K$ of a real Kähler potential. Adding a holomorphic function and its complex conjugate to $K$ leaves the metric unchanged.