A construction of Killing spinors on $Sn$

We derive simple general expressions for the explicit Killing spinors on the n-sphere, for arbitrary n. Using these results we also construct the Killing spinors on various $AdS×Sphere$ supergravity backgrounds, including $AdS5×S5,$ $AdS4×S7,$ and $AdS7×S4.$ In addition, we extend previous results to obtain the Killing spinors on the hyperbolic spaces $Hn.$