A NOTE ON RIEMANNIAN METRICS ON THE MODULI SPACE OF RIEMANN SURFACES

作者：Wu Yunhui^*

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144(6): 2513-2519.

DOI：10.1090/proc/12936

• Moduli space
• visibility manifold
• Riemannian metric

In this note we show that the moduli space M(S-g,(n)) of surface S-g,S-n of genus g with n punctures, satisfying 3g + n >= 5, admits no complete Riemannian metric of nonpositive sectional curvature such that the Teichmuller space T(S-g,S-n) is a mapping class group Mod(S-g,S-n)-invariant visibility manifold.