Old\v rich Kowalski, Zden\v {e}k Vl\'a\v sek
On the local moduli space of locally homogeneous affine connections in plane domains

Abstract:Classification of locally homogeneous affine connections in two dimensions is a nontrivial problem. (See [5] and [7] for two different versions of the solution.) Using a basic formula by B. Opozda, [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).

Keywords: two-dimensional manifolds with affine connection, locally homogeneous connections
AMS Subject Classification: 53B05, 53C30

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