We give a full classification of general affine connections on Galilei manifolds in terms of independently specifiable tensor fields. This generalises the well-known case of (torsional) Galilei connections, i.e. connections compatible with the metric structure of the Galilei manifold. Similarly to the well-known pseudo-Riemannian case, the additional freedom for connections that are not metric-compatible lies in the covariant derivatives of the two tensors defining the metric structure (the clock form and the space metric), which however are not fully independent of each other.

中文翻译：

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牛顿-卡坦几何中一般仿射连接的分类：朝向公制仿射牛顿-卡坦引力


我们根据可独立指定的张量场对 Galilei 流形上的一般仿射连接进行了完整分类。这概括了众所周知的（扭转）伽利莱连接的情况，即与伽利莱流形的公制结构兼容的连接。与众所周知的伪黎曼情况类似，与度量不兼容的连接的附加自由度在于定义度量结构（时钟形式和空间度量）的两个张量的协变导数，但它们并不完全相互独立。