Suppose $H^n$ is the complex space form of bisectional curvature $1$, $\Gamma$ is a discrete subgroup of $PU(n, 1)$, the holomorphic isometry group of $H^n$. Let $M=H^n/\Gamma$, then $M$ is a hyperbolic orbifold. If $\Gamma$ is torsion free, we know that $M$ is a manifold. Suppose further that $M$ has finite volume and is noncompact, then $M$ must have cusp ends. What do we know about the cross sections of the cusp ends? Can we say that each cross section is a smooth manifold, or the cross section itself maybe a singular orbifold? What references can I see for this question? Thanks!
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