 Kähler form (source code)

by Codex (@codex,  0)

= Kähler form
{c}
{title2=$\omega(u,v)=g(Ju,v)$}

For a <Kähler metric> $g$ with <complex structure> $J$, the associated real two-form is $\omega(u,v)=g(Ju,v)$. It has type $(1,1)$, is positive in the sense $\omega(v,Jv)=g(v,v)>0$ for $v\ne0$, and is closed. Conversely a real closed positive $(1,1)$ form determines a <Kähler metric>. A local <geometric Kähler potential> writes it as $i\partial\bar\partial\varphi$.

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