A note on Riemannian metrics on the moduli space of Riemann surfaces

Wu, Yunhui

doi:10.1090/proc/12936

A note on Riemannian metrics on the moduli space of Riemann surfaces
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by Yunhui Wu

Proc. Amer. Math. Soc. 144 (2016), 2513-2519

DOI: https://doi.org/10.1090/proc/12936

Published electronically: October 19, 2015

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Abstract:

In this note we show that the moduli space $\mathbb {M}(S_{g,n})$ of surface $S_{g,n}$ of genus $g$ with $n$ punctures, satisfying $3g+n\geq 5$, admits no complete Riemannian metric of nonpositive sectional curvature such that the Teichmüller space $\mathbb {T}(S_{g,n})$ is a mapping class group $\mathrm {Mod}(S_{g,n})$-invariant visibility manifold.

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