Average Curvatures of Weil-Petersson Geodesics In Teichmüller Space
نویسنده
چکیده
Every point in Teichmüller space is a hyperbolic metric on a given Riemann surface, therefore, a Weil-Petersson geodesic in Teichmüller space can be viewed as a 3-manifold. We investigate the sectional curvatures of this 3-manifold, with a natural metric. We obtain explicit formulas for the curvature tensors of this metric, and show that the “average”s of them are zero, and hence the geometry of this 3-manifold reflects both positive and negative curvatures.
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