We consider sub-Riemannian spaces admitting an isometry group that is maximal in the sense that any linear isometry between the horizontal tangent spaces is realized by a global isometry. We will show that these spaces have a canonical choice of partial connection on their horizontal bundle, which is determined by isometries and generalizes the Levi–Civita connection for the special case of Riemannian model spaces. The number of invariants needed to describe model spaces with the same tangent cone is in general greater than one, and these invariants are not necessarily related to the holonomy of the canonical connections.

中文翻译：

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次黎曼几何中的模型空间

我们认为准黎曼空间允许一个等距组，在某种意义上说，水平切线空间之间的任何线性等距都是通过全局等距实现的。我们将证明这些空间在其水平束上具有规范的部分连接选择，这由等距性确定，并针对黎曼模型空间的特殊情况推广了Levi-Civita连接。描述具有相同切线圆锥的模型空间所需的不变数通常大于1，并且这些不变数不一定与规范连接的完整性相关。