Curvature properties of Teichmüller’s space
Curvature properties of Teichmüller’s space
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Teichmüller 空间的曲率性质
DOI：
10.1007/bf02795342
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发表时间：
1961
期刊：
影响因子：
--
通讯作者：
L. Ahlfors
中科院分区：
文献类型：
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作者：
L. Ahlfors
Teichmuller空间Tg中的一个点由固定亏格g（大于1）的闭黎曼曲面及其基本群的外自同构表示。内禀定义导致了由Teichmuller引入的Tg上的度量，导致了由A. Weil，最后得到3g-3维的复解析结构。它是由韦尔证明的，并且用很少的计算，再次证明了黎曼度量是关于复结构的卡勒度量。推测度量具有负曲率是合理的。主要目的是证明Ricci曲率确实是负的。证明是通过明确的计算。（作者）。
A point in Teichmuller's space Tg is represented by a closed Riemann surface of fixed genus g (is greater than 1) together with an outer automorphism of its fundamental group. Intrinsic definitions lead to a metric on Tg, introduced by Teichmuller, to a Riemannian structure whose use was suggested by A. Weil, and finally to a complex analytic structure of dimension 3g-3. It was proved by Weil, and with very little computation, it is proved again that the Riemannian metric is Kahlerian with respect to the complex structure. It was reasonable to conjecture that the metric has negative curvature. The main purpose of the work is to verify that the Ricci curvatures are indeed negative. The proof is by explicit computations.(Author).