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Journals / International Electronic Journal of Geometry / 2026 / Volume: 14 Issue: 1

On the Moduli Space of Flat Tori Having Unit Area

İsmail Sağlam(Adana Alparslan Türkeş Bilim ve Teknoloji Üniversitesi)0000-0002-1283-6396
Pages
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Publication Date
2021-04-15
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We show that these two metrics coincide.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Inspiring from Thurston's asymmetric metric on Teichmüller spaces, we define and study a natural (weak) metric on the Teichmüller space of the torus.
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Key Findings & Data:We prove that this weak metric is indeed a metric: it separates points and it is symmetric.
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Conclusion & Impact:We show that these two metrics coincide.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:weak metric · asymmetric metric · Teichmüller space

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.

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Cite This Article

Sağlam, İ. (2021). On the Moduli Space of Flat Tori Having Unit Area. International Electronic Journal of Geometry, Volume: 14 Issue: 1. https://doi.org/10.36890/iejg.754478

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