# what is the metric of N-sheeted $AdS_3$?

Suppose the AdS$_3$ metric is given by $$ds^2 =d\rho^2+cosh^2\rho d\psi^2 +sinh^2 \rho d\phi^2$$

what is the n-sheeted space of it? Can the n-sheeted BTZ be constructed from it by identifications as $n=1$ case?