  We gave a new very simple proof that the completion of the space of the
diffeomorphism of the circle modulo conformal maps with respect to the
Weil-Petersson Metric is a complex analytic manifold modeled on the Hilbert
space with 3/2 Sobolev norm. Our proof is based on the analogue of the Hadamard
Theorem that the exponentila map is a complex analytic map from the tanegnt
space of a point of a simply connected manifold to the manifold.
