IUMJ

Title: Curvatures on the Teichmueller curve

Authors: Ren Guo, Subhojoy Gupta and Zheng Huang

Issue: Volume 60 (2011), Issue 5, 1673-1692

Abstract:

The Teichm\"uller curve is the fiber space over Teichm\"uller space $T_g$ of closed Riemann surfaces, where the fiber over a point $(\Sigma,\sigma) \in T_g$ is the underlying surface $\Sigma$. We derive formulas for sectional curvatures on the Teichm\"uller curve. In particular, our method can be applied to investigate the geometry of the Weil-Petersson geodesic as a 3-manifold, and the degeneration of the curvatures near the infinity of the augmented Teichm\"uller space along a Weil-Petersson geodesic, as well as the minimality of hyperbolic surfaces in this 3-manifold.