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