Sag?lam, İsmail2025-01-062025-01-0620211307-562410.36890/IEJG.7544782-s2.0-85108529512https://doi.org/10.36890/IEJG.754478https://search.trdizin.gov.tr/tr/yayin/detay/461840https://hdl.handle.net/20.500.14669/1603Inspiring 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. Our main strategy to do this is to compute the metric explicitly. 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. © 2021eninfo:eu-repo/semantics/openAccessasymmetric metricflat metrichyperbolic metricTeichmüller spacetorusweak metricArticle651Q45946184014