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Dergiler / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

On the Moduli Space of Flat Tori Having Unit Area

İsmail SAĞLAM
Sayfa
59–65
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We show that these two metrics coincide.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri:We prove that this weak metric is indeed a metric: it separates points and it is symmetric.
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Sonuç & Katkı:We show that these two metrics coincide.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

SAĞLAM, İ. (2022). On the Moduli Space of Flat Tori Having Unit Area. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 59–65. https://ajindex.com/articles/539564

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Kaynakça (8)

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  3. Greenfield, M., Ji, L.: Metrics and compactifications of Teichmüller spaces of flat tori. Preprint arXiv:1903.10655. (2019)
  4. Greenfield, M.: A new modular characterization of the hyperbolic plane. Preprint arXiv:1707.00818. (2017)
  5. Sağlam, İ.: Complete flat cone metrics on punctured surfaces. Turkish Journal of Mathematics; 43, 813-832 (2019)
  6. Thurston, W.P.: Minimal Stretch maps between hyperbolic surfaces. Preprint arxiv:9801039. (1985)
  7. Troyanov, M.: Les surfaces euclidienne a singularites coniques, L’Enseign. Math. 32 79–94 (1986)
  8. Troyanov, M.: On the moduli space of singular Euclidean surfaces. In: Handbook of Teichmüller Theory, Vol. 1 (European Mathematical Society). 507–540 (2007).