Tangent spaces of the Teichmüller space of the torus with Thurston's weak metric

Författare

  • Hideki Miyachi Kanazawa University, College of Science and Engineering, School of Mathematics and Physics
  • Ken'ichi Ohshika Gakushuin University, Department of Mathematics
  • Athanase Papadopoulos Université de Strasbourg et CNRS, Institut de Recherche Mathématique Avancée

Nyckelord:

Thurston metric, Teichmüller space, Teichmüller metric, Finsler manifold

Abstract

In this paper, we show that the analogue of Thurston's asymmetric metric on the Teichmüller space of flat structures on the torus is weak Finsler and we give a geometric description of its unit circle at each point in the tangent space to Teichmüller space. We then introduce a family of weak Finsler metrics which interpolate between Thurston's asymmetric metric and the Teichmüller metric of the torus (which coincides with the hyperbolic metric). We describe the unit tangent circles of the metrics in this family.
Sektion
Articles

Publicerad

2022-01-21

Referera så här

Miyachi, H., Ohshika, K., & Papadopoulos, A. (2022). Tangent spaces of the Teichmüller space of the torus with Thurston’s weak metric. Annales Fennici Mathematici, 47(1), 325–334. https://doi.org/10.54330/afm.113702