标题： 牛顿-卡特兰几何中一般仿射联络的分类：迈向度量affine牛顿-卡特兰引力 显示英文标题

标题： The classification of general affine connections in Newton--Cartan geometry: Towards metric-affine Newton--Cartan gravity

摘要： 我们以独立可指定的张量场的形式，给出了伽利略流形上一般仿射联络的完全分类。 这推广了众所周知的（有挠的）伽利略联络情形，即与伽利略流形的度量结构相容的联络。 类似于熟知的伪黎曼情形，非度量相容联络的额外自由度在于定义度量结构的两个张量（时钟形式和空间度量）的协变导数，但它们之间并非完全相互独立。 显示英文摘要

摘要： 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.