论文标题
Teichm {ü}的切线空间与Thurston的弱度量
Tangent spaces of the Teichm{ü}ller space of the torus with Thurston's weak metric
论文作者
论文摘要
在本文中，我们表明，瑟斯顿在teichm {ü} teichm {ü} ller空间上的不对称度量的类似物是弱的鳍片，我们对其单位球体的几何描述在切线空间中的每个点上的几何描述到teichm {ü} ller空间。然后，我们介绍了一个弱的芬斯勒指标家族，该家族在Thurston的不对称度量与Teichm {ü} ller teichm {ü} ller指标之间插值（与双曲线指标一致）。我们描述了这个家庭中指标的无限单位球体。本文的最终版本将出现在AnnalesAcademiæ\ScientiarumFennicæ\ Mathematica中。
In this paper, we show that the analogue of Thurston's asymmetric metric on the Teichm{ü}ller space of flat structures on the torus is weak Finsler and we give a geometric description of its unit sphere at each point in the tangent space to Teichm{ü}ller space. We then introduce a family of weak Finsler metrics which interpolate between Thurston's asymmetric metric and the Teichm{ü}ller metric of the torus (which coincides with the the hyperbolic metric). We describe the infinitesimal unit spheres of the metrics in this family.The final version of this paper will appear in Annales Academiæ \ Scientiarum Fennicæ\ Mathematica.
