Abstract
Fix a number $g \gt 1$, let $S$ be a close surface of genus $g$, and let $\mathrm{Teich}(S)$ be the Teichmüller space of $S$ endowed with the Weil-Petersson metric. In this paper we show that the Riemannian sectional curvature operator of $\mathrm{Teich}(S)$ 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 $\mathrm{Teich}(S)$ is a constant.
Citation
Yunhui Wu. "The Riemannian sectional curvature operator of the Weil-Petersson metric and its application." J. Differential Geom. 96 (3) 507 - 530, March 2014. https://doi.org/10.4310/jdg/1395321848
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