ON A DISTANCE DEFINED BY THE LENGTH SPECTRUM ON TEICHM
ON A DISTANCE DEFINED BY THE LENGTH SPECTRUM ON TEICHM
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发表时间：
2003
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通讯作者：
Uller Space;H. Shiga
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作者：
Uller Space;H. Shiga
我们考虑双曲˜曲面S_0的Teichm Riemann-uller空间T(S_0)上的距离dL。距离被T(S0)中黎曼曲面的长度谱所折减，我们称之为T(S0)上的长度谱度量。如果S_0是拓扑光滑的黎曼曲面，则距离dL决定了与Teichm度量相同的拓扑。本文证明了T(S0)上的长度谱距离dL不偏离与Teichm距离相同的拓扑结构，且存在一个非对称的Riemann曲面S0。我们还给出了这些距离在T(S0)上具有相同拓扑的充分条件。
We consider a distance dL on the Teichm˜ uller space T (S0) of a hyperbolic Riemann surface S0 . The distance is deflned by the length spectrum of Riemann surfaces in T (S0) and we call it the length spectrum metric on T (S0) . It is known that the distance dL determines the same topology as that of the Teichmmetric if S0 is a topologically flnite Riemann surface. In this paper we show that there exists a Riemann surface S0 of inflnite type such that the length spectrum distance dL on T (S0) does not deflne the same topology as that of the Teichmdistance. Also, we give a su-cient condition for these distances to have the same topology on T (S0) .