Flat affine manifolds and their transformations

  title={Flat affine manifolds and their transformations},
  author={Alberto Abad Medina and Omar A. Saldarriaga and A. Villabon},
  journal={arXiv: Differential Geometry},
We give a characterization of flat affine connections on manifolds by means of a natural affine representation of the universal covering of the Lie group of diffeomorphisms preserving the connection. From the infinitesimal point of view, this representation is determined by the 1-connection form and the fundamental form of the bundle of linear frames of the manifold. We show that the group of affine transformations of a real flat affine $n$-dimensional manifold, acts on $\mathbb{R}^n$ leaving… 
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