Curvatures on the Teichmueller curve
Ren GuoSubhojoy GuptaZheng Huang
32G1553C4353C21Teichmueller spaceTeichmueller curvesectional curvatureWeil-Petersson geodesic
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.
Indiana University Mathematics Journal
2011
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10.1512/iumj.2011.60.4443
10.1512/iumj.2011.60.4443
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Indiana Univ. Math. J. 60 (2011) 1673 - 1692
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