A classification of locally homogeneous affine connections on compact   surfaces
  We classify the affine connections on compact orientable surfaces for which the pseudogroup of local isometries acts transitively. We prove that such a connection is either torsion-free and flat, the Levi-Civita connection of a Riemannian metric of constant curvature or the quotient of a translation-invariant connection in the plane. 
Adolfo Guillot and Antonia S\'anchez Godinez
math.DG