Hyperuniform point sets on projective spaces

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