  We prove that the set of closed finite gap curves in hyperbolic 3-space
$\mathbb{H}^3$ is $W^{2,2}$-dense in the Sobolev space of all closed
$W^{2,2}$-curves in $\mathbb{H}^3$. We also show that the set of closed finite
gap curves in any 2-dimensional space form $\mathbb{E}^2$ is $W^{2,2}$-dense in
the Sobolev space of all closed $W^{2,2}$-curves in $\mathbb{E}^2$.
