On the Moduli Space of Flat Tori Having Unit Area

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International Electronic Journal of Geometry
Volume:14 Issue:1
On the Moduli Space of Flat Tori Having Unit Area

On the Moduli Space of Flat Tori Having Unit Area

Pages : 59-65

View : 44 | Download : 11

Publication Date : 2021-04-15

Article Type : Research Paper

Abstract :Inspiring from Thurston`s asymmetric metric on Teichmüller spaces, we define and study a natural insert ignore into journalissuearticles values(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

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