A teleparallel geometry is an n-dimensional manifold equipped with a frame basis and an independent spin connection. For such a geometry, the curvature tensor vanishes and the torsion tensor is non-zero. A straightforward approach to characterizing teleparallel geometries is to compute scalar polynomial invariants constructed from the torsion tensor and its covariant derivatives. An open question has been whether the set of all scalar polynomial torsion invariants, ${\mathcal{I}}_T$, uniquely characterize a given teleparallel geometry. In this paper, we show that the answer is no and construct the most general class of teleparallel geometries in four dimensions, which cannot be characterized by ${\mathcal{I}}_T$. As a corollary, we determine all teleparallel geometries, have vanishing scalar polynomial torsion invariants.

中文翻译：

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不以标量多项式扭转不变量为特征的远平行几何

Teleparallel 几何是一个n维流形，配备了一个框架基础和一个独立的自旋连接。对于这样的几何形状，曲率张量消失并且扭转张量非零。表征遥平行几何的一种直接方法是计算由扭转张量及其协变导数构成的标量多项式不变量。一个悬而未决的问题是所有标量多项式扭转不变量的集合是否，${\mathcal{一世}}_{吨}$唯一地表征给定的Teleparallel几何形状。在本文中，我们证明答案是否定的，并在四个维度上构建了最通用的远程平行几何类别，其特征不能为${\mathcal{一世}}_{吨}$. 作为推论，我们确定所有远平行几何，具有消失的标量多项式扭转不变量。