Asymptotic Flatness of the Weil–Petersson Metric on Teichmüller Space
نویسنده
چکیده
In this paper, we show that there is no negative upper bound for the sectional curvature of Teichmüller space of Riemann surfaces with the Weil–Petersson metric. Mathematics Subject Classifications (2000). 32G15, 53C21, 30F60.
منابع مشابه
On Asymptotic Weil-Petersson Geometry of Teichmüller Space of Riemann Surfaces
We investigate the asymptotic behavior of curvatures of the Weil-Petersson metric in Teichmüller space. We use a pointwise curvature estimate to study directions, in the tangent space, of extremely negative curvature and directions of asymptotically zero curvatures.
متن کاملAverage Curvatures of Weil-Petersson Geodesics In Teichmüller Space
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 o...
متن کاملWeil-Petersson geometry of Teichmüller–Coxeter complex and its finite rank property
Resolving the incompleteness of Weil-Petersson metric on Teichmüller spaces by taking metric and geodesic completion results in two distinct spaces, where the Hopf-Rinow theorem is no longer relevant due to the singular behavior of the Weil-Petersson metric. We construct a geodesic completion of the Teichmüller space through the formalism of Coxeter complex with the Teichmüller space as its non...
متن کاملWeil-petersson Metric on the Universal Teichmüller Space I: Curvature Properties and Chern Forms
We prove that the universal Teichmüller space T (1) carries a new structure of a complex Hilbert manifold. We show that the connected component of the identity of T (1), the Hilbert submanifold T0(1), is a topological group. We define a Weil-Petersson metric on T (1) by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that T (1) is a Kähler -Einstei...
متن کاملOn the Weil-petersson Volume and the First Chern Class of the Moduli Space of Calabi-yau Manifolds
In this paper, we continue our study of the Weil-Petersson geometry as in the previous paper [10], in which we have proved the boundedness of the Weil-Petersson volume, among the other results. The main results of this paper are that the volume and the integrations of Ricci curvature of the Weil-Petersson metric on the moduli space are rational numbers. In particular, the Ricci curvature define...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005