- International Electronic Journal of Geometry
- Vol: 14 Issue: 1
- On the Moduli Space of Flat Tori Having Unit Area
On the Moduli Space of Flat Tori Having Unit Area
Authors : Ismail Sağlam
Pages : 59-65
Doi:10.36890/iejg.754478
View : 7 | Download : 4
Publication Date : 2021-04-15
Article Type : Research
Abstract :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.Keywords : weak metric, asymmetric metric, Teichmüller space, torus, flat metric, hyperbolic metric