Flat affine manifolds and their transformations

@article{Medina2019FlatAM,
title={Flat affine manifolds and their transformations},
author={Alberto Abad Medina and Omar A. Saldarriaga and A. Villabon},
journal={arXiv: Differential Geometry},
year={2019}
}
• Published 9 October 2019
• Mathematics
• 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…
1 Citations

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