Weil-Petersson metric on the universal Teichmuller space I: Curvature properties and Chern forms
| dc.creator | Takhtajan, Leon A. | |
| dc.creator | Teo, Lee-Peng | |
| dc.date | 2003-12-08 | |
| dc.date | 2004-06-21 | |
| dc.date.accessioned | 2026-07-07T05:03:40Z | |
| dc.date.available | 2026-07-07T05:03:40Z | |
| dc.description | 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. | |
| dc.description | 70 pages, appendix A added | |
| dc.identifier | https://arxiv.org/abs/math/0312172 | |
| dc.identifier | http://arxiv.org/abs/math/0312172 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69517 | |
| dc.subject | Complex Variables | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Differential Geometry | |
| dc.subject | 30F60 (Primary) 32G15, 46E20, 58B20, 58B25 (Secondary) | |
| dc.title | Weil-Petersson metric on the universal Teichmuller space I: Curvature properties and Chern forms | |
| dc.type | text |