Killing spinor equations are equations that result from supersymmetric transformations. One example of those is for example is in $N=2$ Supergravity theories.
As suggested by some books and papers on the web, there is the vanishing of the gravitini supersymmetry.
So if fermions here should vanish in $N=2$ supergravity theories, what KSE's should we see in $N=2$ sugra?