Averaging Kähler forms over a complex torus
= Averaging Kähler forms over a complex torus
{title2=$\omega_0=\int_Tt_a^*\omega\,da$}
Averaging a <Kähler form> over translations with normalized <Haar measure> gives an invariant <Kähler form> in the same <de Rham cohomology> class. Positivity is preserved by averaging positive values on $(v,Jv)$, and the class is unchanged because translations are homotopic to the identity. Thus any <Hodge metric> on a <complex torus> can be replaced by an invariant one.