RESUMEN

It is shown that the unique homogeneous Kähler metric carried by M = Diff (S¹)/SL(2,R) induces the weil-Peterson metric on the Teichmüller space T(1). The identification was obtained in [12] simply by noting that every diffeomorphism of S¹ is a quasisymetric homeomorphism. Our computations allow us also to prove that every T(G), G any infinite Fuchsian group, projects out of M transversely. This last assertion is related to the “fractal” nature of G-invariant quasicircles.