On the Moduli Space of Flat Tori Having Unit Area
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Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
DergiPark
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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. 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. © 2021
Açıklama
Anahtar Kelimeler
asymmetric metric, flat metric, hyperbolic metric, Teichmüller space, torus, weak metric
Kaynak
International Electronic Journal of Geometry
WoS Q Değeri
Scopus Q Değeri
Q4
Cilt
14
Sayı
1
