  We prove that the universal Teichmuller space T(1) carries a new structure of
a complex Hilbert manifold. We show that the connected component of the
identity of T(1), the Hilbert submanifold T_{0}(1), is a topological group. We
define a Weil-Petersson metric on T(1) by Hilbert space inner products on
tangent spaces, compute its Riemann curvature tensor, and show that T(1) is a
Kahler-Einstein manifold with negative Ricci and sectional curvatures. We
introduce and compute Mumford-Miller-Morita characteristic forms for the
vertical tangent bundle of the universal Teichmuller curve fibration over the
universal Teichmuller space. As an application, we derive Wolpert curvature
formulas for the finite-dimensional Teichmuller spaces from the formulas for
the universal Teichmuller space.
