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Apr 2, 2010 at 20:53 vote accept Botong Wang
Apr 1, 2010 at 0:03 comment added Dylan Thurston The Riemannian metric came from the original hyperbolic metric: you started with the assumption you had $\Gamma$ acting on $H$ so the quotient had finite measure. A Riemannian metric on a 2-manifold gives you a conformal structure, where multiplication by $i$ is rotation by $90$ degrees.
Mar 31, 2010 at 21:19 comment added Botong Wang Thanks for your answer too. I am not sure how is the Riemannian metric obtained? Do you just choose one which gives finite measure? Is there any relation with the conformal structure?
Mar 30, 2010 at 6:27 history answered Dylan Thurston CC BY-SA 2.5