Inspiring from Thurston's asymmetric metric on Teichmüller spaces, we define and study a natural (weak) metric on the Teichmüller space of the torus. We prove that this weak metric is indeed a metric: it separates points and it is symmetric. We relate this metric with the hyperbolic metric on the upper half-plane. We define another metric which measures how much length of a closed geodesic changes when we deform a flat structure on the torus. We show that these two metrics coincide.
weak metric asymmetric metric Teichmüller space torus flat metric hyperbolic metric
Birincil Dil | İngilizce |
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Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Yayımlanma Tarihi | 15 Nisan 2021 |
Kabul Tarihi | 15 Ekim 2020 |
Yayımlandığı Sayı | Yıl 2021 Cilt: 14 Sayı: 1 |