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arXiv · 1501.02875

The Riemannian Sectional Curvature Operator Of The Weil-Petersson Metric and Its Application

Yunhui Wu
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Abstract

Fix a number $g>1$, let $S$ be a close surface of genus $g$, and $Teich(S)$ be the Teichm\"uller space of $S$ endowed with the Weil-Petersson metric. In this paper we show that the Riemannian sectional curvature operator of $Teich(S)$ is non-positive definite. As an application we show that any twist harmonic map from rank-one hyperbolic spaces $H_{Q,m}=Sp(m,1)/Sp(m)\cdot Sp(1)$ or $H_{O,2}=F_{4}^{-20}/SO(9)$ into $Teich(S)$ is a constant.

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Yunhui Wu. 2015-01-13. The Riemannian Sectional Curvature Operator Of The Weil-Petersson Metric and Its Application. https://doi.org/10.4310/jdg%2F1395321848

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