Flat Affine Manifolds And Their Transformations

14 Oct 2020 Medina A. Saldarriaga O. Villabon A.

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... (read more)

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  • DIFFERENTIAL GEOMETRY