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The Riemannian sectional curvature operator of the Weil-Petersson metric and Its application

Yunhui Wu Tsinghua University

Geometric Analysis and Geometric Topology mathscidoc:1904.15001

Journal of Differential Geometry, 96, (3), 507-530, 2014
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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@inproceedings{yunhui2014the,
  title={The Riemannian sectional curvature operator of the Weil-Petersson metric and Its application},
  author={Yunhui Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190430205313802427302},
  booktitle={Journal of Differential Geometry},
  volume={96},
  number={3},
  pages={507-530},
  year={2014},
}
Yunhui Wu. The Riemannian sectional curvature operator of the Weil-Petersson metric and Its application. 2014. Vol. 96. In Journal of Differential Geometry. pp.507-530. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190430205313802427302.
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