A definite triple $\bm{\underline{\omega}}$ is said

1. (i)

   closed if $d\omega_{i}=0$ for $i=1,2,3$;

2. (ii)

   an $SU(2)$–structure if $Q_{\bm{\underline{\omega}}}\equiv\text{id}$;

3. (iii)

   hyperkähler if it is both closed and an $SU(2)$–structure.