Geodesic
On the local moduli space of locally homogeneous affine connections in plane domains
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 2, pp. 229-234

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Classification of locally homogeneous affine connections in two dimensions is a nontrivial problem. (See \cite{5} and \cite{7} for two different versions of the solution.) Using a basic formula by B. Opozda, \cite{7}, we prove that all locally homogeneous torsion-less affine connections defined in open domains of a 2-dimensional manifold depend essentially on at most 4 parameters (see Theorem 2.4).
Classification : 53B05, 53C30
Keywords: two-dimensional manifolds with affine connection; locally homogeneous connections 
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Kowalski, Oldřich; Vlášek, Zdeněk. On the local moduli space of locally homogeneous affine connections in plane domains. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 2, pp. 229-234. http://geodesic.mathdoc.fr/item/CMUC_2003__44_2_a3/