“…It is shown that the Weil-Petersson metric is Kählerian ([1]), with negative sectional curvature ( [19], [24]). The Weil-Petersson Riemannian curvature tensor is given as the TrombaWolpert formula ( [19], [24]): [22]). This is caused by pinching off at least one short closed geodesic on the surface.…”
Abstract. In the thick part of the moduli space of Riemann surfaces, we show that the sectional curvature of the Weil-Petersson metric is bounded independently of the genus of the surface.
“…In [3] and [4], the authors posed the problem of developing a means by which one can study the resulting Arakelov-induced metric on M g . Specifically, it is asked if the Arakelov-induced metric on the moduli space M g is complete or not, which in the case of the classical Weil-Petersson metric was first answered in [13] and [11].…”
Section: Arakelov Metrics On Riemann Surfacesmentioning
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