The Riemannian Sectional Curvature Operator of the Weil-petersson Metric and Its Application
نویسنده
چکیده
Fix a number g > 1, let S be a close surface of genus g and 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 Teich(S) is non-positive definite. As an application we show that any twist harmonic map from rank-one hyperbolic spaces HQ,m = Sp(m, 1)/Sp(m) · Sp(1) or HO,2 = F −20 4 /SO(9) into Teich(S) is a constant.
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تاریخ انتشار 2012