Elliptic stabilizer obstruction to a hyperbolic manifold quotient
= Elliptic stabilizer obstruction to a hyperbolic manifold quotient
A nontrivial finite-order <elliptic Möbius transformation> fixes an axis in <hyperbolic space>. The quotient metric has cone angle $2\pi/m$ along that axis for a stabilizer of order $m$, so it is locally an <orbifold> metric rather than a smooth hyperbolic-manifold metric. The underlying topological quotient may nevertheless be a manifold.