  We extend the notion of hyperuniformity to the projective spaces
$\mathbb{RP}^{d-1}$, $\mathbb{CP}^{d-1}$, $\mathbb{HP}^{d-1}$, and
$\mathbb{OP}^2$. We show that hyperuniformity implies uniform distribution and
present examples of deterministic point sets as well as point processes which
exhibit hyperuniform behaviour.
