= Kähler potential
{disambiguate=complex geometry}
{c}
{title2=$\omega=i\partial\bar\partial\varphi$}
= Kähler metric potential
{c}
{synonym}
= Geometric Kähler potential
{synonym}
A <geometric Kähler potential> is locally a real smooth function $\varphi$ with $\omega=i\partial\bar\partial\varphi$ for the <Kähler form>. Its complex Hessian must be positive definite to define a <Kähler metric>. Conventions sometimes absorb a factor of $1/2$ into $\varphi$. Potentials differing by the real part of a <holomorphic function> determine the same form. This topic concerns ordinary <complex geometry>; the existing undisambiguated <Kähler potential> entry concerns superfields.
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