Do there exist compact Riemannian manifolds of constant negative sectional curvature in all dimensions $\geq2$?
The two-dimensional case is well-known. For higher dimensions, this question asks for explicit examples, and it turns out that the construction could be very difficult. But what if I only ask for existence? Is there an easy way to show that that $\mathbb{H}^n$ admits a compact quotient manifold for all $n\geq2$?
Thanks in advance!