Distance and angles between Teichmuller geodesics
Distance and angles between Teichmuller geodesics
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Teichmuller 测地线之间的距离和角度
DOI：
10.1016/j.aim.2019.106892
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发表时间：
2020
影响因子：
1.7
通讯作者：
Zhong Youliang
中科院分区：
文献类型：
--
作者：
Liu Lixin;Su Weixu;Zhong Youliang
我们表明，Teichmüller测地线从一个共同的点，定义使用余弦定律之间的角度，并不总是存在。证明使用有限维Teichmüller空间上的Teichmüller距离的估计。因此，具有Teichmüller度量的Teichmüller空间对任何k∈ R都不是CAT（k）空间。本文还讨论了Teichmüller测地线夹角存在的必要条件。
We show that the angles between Teichmüller geodesic rays issuing from a common point, defined by using the law of cosines, do not always exist. The proof uses an estimation for the Teichmüller distance on finite dimensional Teichmüller spaces. As a consequence, the Teichmüller space equipped with the Teichmüller metric is not a CAT (k) space for any k∈ R. We also discuss some necessary conditions for the existence of angle between the Teichmüller geodesics.