%0 Journal Article
%T Bers isomorphism on the universal Teichm¨šller curve
%A Lee-Peng Teo
%J Mathematics
%D 2006
%I arXiv
%X We study the Bers isomorphism between the Teichm\"uller space of the parabolic cyclic group and the universal Teichm\"uller curve. We prove that this is a group isomorphism and its derivative map gives a remarkable relation between Fourier coefficients of cusp forms and Fourier coefficients of vector fields on the unit circle. We generalize the Takhtajan-Zograf metric to the Teichm\"uller space of the parabolic cyclic group, and prove that up to a constant, it coincides with the pull back of the Velling-Kirillov metric defined on the universal Teichm\"uller curve via the Bers isomorphism.
%U http://arxiv.org/abs/math/0607336v1